Meditaliano IMAT Prep
Lesson 4: Electromagnetism & DC Circuits
Lesson Overview
Welcome to the definitive guide on Electromagnetism. This lesson bridges the gap between abstract field theories and practical applications. We start by building a Mathematical Toolkit to understand vectors and calculus in physics. We then explore the origins of magnetism, the forces it exerts on charged particles (leading to technologies like Mass Spectrometers), and finally, the principle of Induction that powers our civilization.
1. Math Toolkit & Origins
- Dot vs. Cross Products
- The Right-Hand Rules & Fleming's
- Graphical Analysis: Slopes and Areas
- Origin of Magnetism & Domains
- Ferro-, Para-, Diamagnetism
2. Fields & Forces
- B-Fields: Wire, Loop, Solenoid
- Lorentz Force & Circular Motion ($F_c$)
- Medical App: The Hall Effect
- Torque on Loops & Electric Motors
- Forces between parallel wires
3. Induction & Circuits
- Magnetic Flux & Faraday's Law
- Lenz's Law (Conservation of Energy)
- Motional EMF (Rod on Rails)
- Generators (AC vs DC)
- Transformers & RL Circuits
4. Synthesis & Medical
- Maxwell's Equations
- AC Current: RMS & Reactance
- Medical Deep Dive: MRI Physics
- Step-by-Step Solved Problems
Part 1: The Mathematical Toolkit
Magnetism is inherently 3-dimensional. To understand directions and magnitudes, we must master vector operations.
1.1 Vectors: Dot Product vs Cross Product
Dot Product (Scalar Product)
Measures "How much of Vector A is parallel to Vector B". Result is a Number.
$$\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}||\mathbf{B}|\cos\theta$$Physics Applications:
- Work: $W = \mathbf{F} \cdot \mathbf{d} = Fd\cos\theta$ (Only force parallel to distance does work).
- Magnetic Flux: $\Phi = \mathbf{B} \cdot \mathbf{A} = BA\cos\theta$ (Only field parallel to area vector penetrates).
Cross Product (Vector Product)
Measures "How perpendicular Vector A is to Vector B". Result is a Vector perpendicular to both.
$$|\mathbf{A} \times \mathbf{B}| = |\mathbf{A}||\mathbf{B}|\sin\theta$$Physics Applications:
- Lorentz Force: $\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$ (Max force when velocity $\perp$ field).
- Torque: $\mathbf{\tau} = \mathbf{r} \times \mathbf{F}$ (Max torque when force $\perp$ lever arm).
The Cross Product yields a vector orthogonal to the plane defined by vectors A and B.
1.2 Direction Rules: Right-Hand and Left-Hand
Confusion often arises because there are multiple rules to determine 3D direction in electromagnetism. Here is a definitive summary:
1. Right-Hand Grip Rule (Current to Field)
Used for: Finding the magnetic field ($B$) caused by a straight wire carrying current ($I$), OR finding the poles of a solenoid.
Action: Point your Thumb in the direction of the Current ($I$). Your fingers will naturally curl in the direction of the surrounding Magnetic Field ($B$).
2. Fleming's Left-Hand Rule (The Motor Rule)
Used for: Finding the direction of Force ($F$) on a current-carrying wire or moving positive charge placed in an external magnetic field.
Action: Extend your left hand. Thumb = Force (Thrust). First Finger = Magnetic Field. Second Finger = Current (or velocity of positive charge).
Standard 3D Notation Symbols
Because we draw on flat 2D paper, we need symbols to represent vectors pointing directly towards or away from us.
(Like seeing the tail feathers of a dart)
(Like seeing the sharp tip of a dart)
1.3 Rates of Change & Areas: The Language of Physics
Slope ($\Delta y / \Delta x$): Rate of Change
Used when quantities change over time or distance. Graphically, this is the slope.
- Induced EMF: $\mathcal{E} = -\frac{\Delta\Phi}{\Delta t}$ (Rate of change of Flux).
- Current: $I = \frac{\Delta Q}{\Delta t}$ (Rate of flow of charge).
Area Under the Curve: Accumulation
Used to sum up quantities. Instead of complex integrals, we use geometric areas.
- Work done by variable force: Area under the Force vs. Distance graph.
- Impulse: Area under the Force vs. Time graph.
Part 2: Nature of Magnetism & Fields
2.1 The Origin of Magnetism
Magnetism creates forces between moving charges. But what about permanent magnets that sit still on your fridge?
Microscopic Origin: Magnetism arises from the intrinsic quantum Spin of electrons and their Orbital Motion around the nucleus. Each moving electron acts like a tiny loop of current, producing its own minuscule magnetic dipole.
Magnetic Domains: In ferromagnetic materials (like Iron, Nickel, and Cobalt), atomic dipoles group together into regions called "domains" where all spins align. In an unmagnetized piece of iron, these domains point randomly and cancel each other out. In a permanent magnet, the domains are forced to align in the same direction.
Left: Randomly oriented domains (Unmagnetized). Right: Externally applied field forces domains to align, creating a strong permanent magnet.
Classification of Magnetic Materials
Strongly attracted to magnets. Domains align permanently even after external field is removed (Iron, Ni, Co). High permeability $\mu \gg \mu_0$.
Weakly attracted. Random individual spins align slightly with an external field, but lose alignment when removed (Aluminum, Platinum). $\mu \approx \mu_0$.
Weakly repelled. Atoms have no net permanent dipole, but an external field induces an opposing field inside them (Water, Wood, Frog). $\mu < \mu_0$.
2.2 Earth's Magnetic Field (Geomagnetism)
The Earth acts like a giant bar magnet tilted $\approx 11^\circ$ from the rotation axis.
- Magnetic North Pole: Is physically a South magnetic pole (because it attracts the North pole of a compass needle). Located near the geographic North Pole.
- Declination: The angle between geographic True North and Magnetic North.
- Dip (Inclination): The angle the B-field makes with the horizontal surface. $0^\circ$ at the equator, $90^\circ$ straight down at the poles.
2.3 AC vs DC Currents
Direct Current (DC): Constant flow direction (Batteries). Electrons drift slowly in one direction.
Alternating Current (AC): Electrons oscillate back and forth. Energy is transmitted via the wave.
Period ($T$): Time for one complete cycle [s].
Frequency ($f$): Cycles per second [Hz]. $f = 1/T$.
Angular Freq ($\omega$): $\omega = 2\pi f$.
RMS Values: AC voltage and power vary constantly. The effective equivalent DC value is the RMS (Root Mean Square).
$$V_{rms} = \frac{V_{peak}}{\sqrt{2}} \approx 0.707 V_{peak}$$2.4 Magnetic Fields Generated by Currents
Recall the Right-Hand Grip Rule: Thumb = Current $I$, Curled Fingers = B-Field direction.
| Type | Formula | Field Characteristics |
|---|---|---|
| Straight Wire | $B = \frac{\mu_0 I}{2\pi r}$ | Concentric circles around the wire. Weakens with distance ($1/r$). |
| Solenoid (Long Coil) | $B = \mu_0 n I$ | Inside: Uniform, Strong, Parallel lines. Outside: $\approx 0$. ($n = N/L$ turns per length) |
| Circular Loop (Center) | $B = \frac{\mu_0 I}{2R}$ | Field perpendicular to the flat plane of the loop exactly at the center. |
| Toroid (Donut) | $B = \frac{\mu_0 N I}{2\pi r}$ | Confined entirely within the donut shape. No external field. |
Visualizing the magnetic fields around a straight wire, a circular loop, and a solenoid.
$\mu_0 = 4\pi \times 10^{-7} T\cdot m/A$ (Permeability of Free Space).
2.5 Magnetic Flux Density ($B$) vs. Magnetic Field Strength ($H$)
In physics, it is crucial to distinguish between the magnetic field created purely by the external current and the total magnetic field that actually exists inside a material.
- Magnetic Field Strength ($H$): Depends ONLY on the free current generating the field (e.g., for a solenoid, $H = nI$). Measured in Amperes per meter (A/m).
- Magnetic Flux Density ($B$): The actual, total magnetic field felt in the region, which includes the material's own magnetic response. Measured in Tesla (T).
- Permeability ($\mu$): The property of the material that connects them. $\mu_r$ is the relative permeability (how much the material amplifies the field).
Part 3: Forces & High-Tech Applications
3.1 Lorentz Force on Particles
- Direction: Fleming's Left-Hand Rule or Right-Hand Palm Rule. Remember to flip the direction if the charge ($q$) is negative!
- Work: Magnetic force is a cross product, meaning it is always perpendicular ($\perp$) to velocity. Therefore, it can only change direction, not speed. Work done by a static magnetic field is always zero. Kinetic Energy is constant.
Circular Motion & The Lorentz Force
If a particle enters a uniform B-field perpendicularly, the magnetic force is always perpendicular to the velocity vector. In mechanics, a force that is always perpendicular to motion acts as a Centripetal Force ($F_c$), forcing the particle into a uniform circular path.
By equating the Lorentz force to the centripetal force formula ($F_c = \frac{mv^2}{r}$), we can set up the fundamental equation for magnetic circular motion:
Solving for the radius ($r$) of the circular path, we get: $r = \frac{mv}{qB}$
A positively charged particle moving perpendicular to a uniform magnetic field (denoted by the blue crosses $\otimes$ pointing into the page) is deflected into a uniform circular path.
The velocity $v$ and magnetic force $F$ are always at right angles. The magnetic field provides the necessary centripetal force to maintain circular motion.
Cyclotrons & Frequency
Note that the time to complete one circle (Period, $T$) does not depend on velocity or radius! $$T = \frac{2\pi r}{v} = \frac{2\pi m}{qB}$$ This constant period allows cyclotrons to accelerate particles using a fixed frequency alternating voltage.
Challenge an IMAT Question!
Official Paper: 2024 - Q58
worked solution & explanation
Concept Lorentz Force Dynamics. A charged particle entering a magnetic field perpendicularly experiences a force ($F = qvB$) perpendicular to its velocity.
Step 1 A continuous perpendicular force acts as a centripetal force, forcing the particle into uniform circular motion.
Step 2 In uniform circular motion, the particle's *speed* (scalar magnitude) remains constant. However, its *velocity* is a vector. Because the direction is constantly curving, the velocity vector is changing.
Step 3 Therefore, claiming the electron moves with a 'constant velocity' is mathematically false.
Challenge an IMAT Question!
Official Paper: 2024 - Q58
worked solution & explanation
Concept Identical to Q10 in the official papers. Review Q10 for full explanation.
Step 1 Velocity is a vector. Uniform circular motion constantly alters the spatial direction of the velocity vector.
Step 2 The electron's speed remains constant, but stating its 'velocity' is constant is mathematically false.
3.2 Application: The Velocity Selector
Used to filter particles of a specific speed. We apply both an Electric Field ($E$) and Magnetic Field ($B$) perpendicularly so their forces oppose each other.
Magnetic Force $F_B = qvB$
For straight line un-deflected motion: $F_E = F_B \implies qE = qvB$
$$v = \frac{E}{B}$$
3.3 Application: Mass Spectrometer
After selecting velocity, particles enter a region with only a B-field. They curve into a circle. Because $r = \frac{mv}{qB}$, the radius depends heavily on mass $m$.
Heavier ions have larger momentum, so they bend less and have larger radii. This allows us to separate isotopes by mass.
3.4 Deep Dive: The Hall Effect
Medical Relevance: Blood Flow Meters
The Hall Effect is used to measure magnetic field strength (Hall Probe) or fluid flow rates containing ions (like electromagnetic blood flow meters).
When a current (or flowing blood) moves through a magnetic field, the Lorentz force pushes charge carriers to one side of the vessel/conductor. This charge buildup creates a transverse Electric Field (Hall Field) and a measurable voltage difference across the sides (Hall Voltage, $V_H$).
3.5 Force on Currents & The Motor Effect
Since current is a stream of charges, macroscopic wires feel a force too.
$$F = I L B \sin\theta$$Torque on a Current Loop (Electric Motors)
If we place a rectangular loop of wire in a B-field, one side is pushed up, the other down. This creates a turning force (Torque).
- $N$: Number of wire turns in the coil
- $A$: Area of the loop
- $\phi$: Angle between the B-field and the Normal vector (perpendicular) to the loop's surface area.
Force Between Parallel Wires
Wire 1 creates a magnetic field $B_1$, which then exerts a Lorentz force on the charges flowing in Wire 2. This definition is actually how the Ampere (A) was historically defined.
Currents in SAME Direction: ATTRACT
Currents in OPPOSITE Direction: REPEL
Force per unit length: $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$
Challenge an IMAT Question!
Official Paper: 2014 - Q59
worked solution & explanation
Concept Magnetic Repulsion Paradigm. Attraction can be ambiguous, but repulsion is highly specific.
Step 1 Any unmagnetized ferromagnetic material (like soft iron) will ALWAYS be attracted to a magnet via induction. It can never be repelled.
Step 2 Repulsion occurs exclusively between two active, permanent magnetic fields when identical poles face each other.
Step 3 Therefore, the bar must already be an active permanent magnet itself. Magnetized steel fits this perfectly.
Part 4: Electromagnetic Induction & Circuits
4.1 Magnetic Flux ($\Phi$)
We define flux as the number of field lines passing through a specific surface area $A$.
$$\Phi_B = \mathbf{B} \cdot \mathbf{A} = BA\cos\theta \quad [Weber (Wb)]$$4.2 Faraday's Law & Lenz's Law
Faraday's Law of Induction: A changing magnetic flux over time induces an Electromotive Force (EMF, $\mathcal{E}$) in a conductor.
Lenz's Law (The Negative Sign): The induced current creates its own magnetic field that opposes the change in the original magnetic flux. If a North pole is pushed into a coil, the coil induces a North pole to repel it. This perfectly preserves the Conservation of Energy.
Challenge an IMAT Question!
Official Paper: 2022 - Q58
worked solution & explanation
Concept Lenz's Law of Electromagnetic Induction. Induced current opposes the underlying change in magnetic flux.
Step 1 Initial action: N-pole approaches from left. This increases right-pointing flux. Coil induces a left-pointing magnetic field (creates N-pole on left) to repel it.
Step 2 We need an action requiring the coil to also create a left-pointing field. This happens if right-pointing flux increases OR left-pointing flux decreases.
Step 3 Inserting an S-pole into the right side brings its inward-pointing field closer. From the coil's perspective, this increases right-pointing flux. The coil reacts identically.
Challenge an IMAT Question!
Official Paper: 2011 - Q73
worked solution & explanation
Concept Ohm's Law with internal/fixed circuit resistance: $I = \frac{V}{R_{\text{fixed}} + R_{\text{variable}}}$.
Step 1 When the variable resistance ($R$) is exactly $0$, the current is $I = V / R_{\text{fixed}}$. This is a finite, non-zero maximum value. Therefore, the graph must intercept the y-axis at a positive number.
Step 2 As $R$ increases, $I$ must decrease. Because $R$ is in the denominator of a fraction with a constant added term, the relationship is a mathematical hyperbola (a $y = 1/x$ type curve), not a straight line.
Step 3 Graph C correctly shows a non-zero y-intercept curving smoothly downwards.
4.3 Deep Dive: Motional EMF
Consider a conducting metallic rod of length $L$ moving with velocity $v$ along conductive rails in a uniform magnetic field $B$.
Motional EMF: As the rod moves through the magnetic field, its internal free electrons feel a Lorentz force pushing them to one end. This separates the charge, creating a potential difference across the rod, essentially turning it into a moving battery.
4.4 Generators: Turning Work into Electricity
If we manually rotate a coil inside a B-field, the angle changes continuously, meaning the flux changes periodically.
The maximum (peak) induced EMF depends on the number of turns ($N$), magnetic field ($B$), area ($A$), and angular velocity ($\omega$):
This sinusoidal output produces Alternating Current (AC) naturally. To extract DC from a generator, we must use a Split Ring Commutator.
4.5 Eddy Currents
When a bulk solid conductor (like a solid metal plate) moves through a magnetic field, the changing flux induces circulating loops of current within the metal body called Eddy Currents.
By Lenz's law, these currents create magnetic fields opposing the motion, causing magnetic drag (braking systems in trains). The resistance in the metal also turns the current into massive amounts of heat (used in induction cooktops).
4.6 Transformers (Mutual Induction)
Transformers are devices used to step-up (increase) or step-down (decrease) AC voltage for power transmission. They only work with AC because induction requires a constantly changing magnetic flux.
An alternating current in the Primary Coil induces a constantly changing magnetic field in the iron core. This changing field travels through the core and induces an alternating EMF in the Secondary Coil.
Ideal Transformer Principle: Power Input = Power Output ($I_p V_p = I_s V_s$). If you step up voltage, you must step down current proportionally to conserve energy.
Challenge an IMAT Question!
Official Paper: 2012 - Q73
1. thermal
2. chemical
3. magnetic
worked solution & explanation
Concept Definition of Superconductivity and current effects.
Step 1 Statement 1 (False): By strict definition, a superconductor has precisely zero electrical resistance ($R=0$). Since thermal Joule heating is $P = I^2R$, zero resistance means zero heat is generated.
Step 2 Statement 2 (False): Chemical effects (electrolysis) require chemical solutions. Pure mercury acts as a solid conductor with no chemical alteration from current.
Step 3 Statement 3 (True): Biot-Savart Law dictates that *any* moving electric charge invariably generates a magnetic field, regardless of the material's resistance.
4.7 Self-Inductance & RL Circuits
When current passes through a coil, it creates a magnetic flux through itself. If the current changes, the flux changes, inducing an EMF that fights the change in its own current. This property is Inductance ($L$), measured in Henrys (H).
$$\mathcal{E}_{back} = -L \frac{\Delta I}{\Delta t}$$Energy stored in an Inductor's magnetic field: $U = \frac{1}{2}LI^2$.
Challenge an IMAT Question!
Official Paper: 2013 - Q55
1. Use more turns of wire in the coil
2. Use thicker wire
3. Change the speed of rotation
worked solution & explanation
Concept Faraday's Law of Induction for Generators. The generated EMF (voltage) is governed by $\varepsilon = N \cdot A \cdot B \cdot \omega \cdot \sin(\omega t)$.
Step 1 Statement 1 (True): $N$ is the number of turns. Increasing $N$ directly mathematically scales the generated voltage.
Step 2 Statement 3 (True): $\omega$ is the angular speed of rotation. Rotating it faster directly multiplies the voltage peak.
Step 3 Statement 2 (False): Thicker wire alters internal resistance, allowing higher *current* without overheating, but has absolutely zero effect on the pure induced *voltage* potential.
Part 5: Synthesis & Medical Applications
5.1 Maxwell's Equations (Qualitative)
James Clerk Maxwell unified electricity and magnetism into 4 core mathematical statements, predicting that light itself is an electromagnetic wave. This is the pinnacle of Classical Physics.
1. Gauss's Law for Electricity: Electric charges create divergent E-fields. (Positive charges are sources, negative are sinks. Electric monopoles exist).
2. Gauss's Law for Magnetism: There are no magnetic monopoles. Magnetic field lines are continuous loops ($\oint B \cdot dA = 0$). If you cut a magnet in half, you get two smaller magnets, not isolated N and S poles.
3. Faraday's Law of Induction: A changing magnetic field creates an electric field.
4. Ampere-Maxwell Law: Moving charges (currents) OR a changing electric field will create a magnetic field.
5.2 Medical Deep Dive: MRI Physics
How Magnetic Resonance Imaging Works
MRI is the ultimate medical application of quantum mechanics and electromagnetism, producing incredibly detailed soft-tissue images without dangerous ionizing radiation.
- Alignment: The patient enters a massive superconducting solenoid ($B \approx 1.5 - 3.0$ Tesla). Protons (Hydrogen nuclei in water and fat) align their magnetic spins parallel or anti-parallel with this massive B-field.
- Resonance (Excitation): A Radio Frequency (RF) pulse is sent into the tissue at the precise Larmor Frequency. This energy flips the protons away from their aligned state.
- Relaxation: The RF pulse stops. The protons "relax" back to alignment with the main B-field. As they do, they emit their own RF signals.
- Detection: Gradient coils vary the magnetic field slightly across different regions of the body ($B(x)$). Because the resonant frequency depends on the local B-field strength, the computer can use Fourier transforms to pinpoint exactly where each signal originated, constructing a 3D image based on tissue water content.
Part 6: Master Solved Problems
Problem 1: The Mass Spectrometer
A proton ($q=1.6 \times 10^{-19} C, m=1.67 \times 10^{-27} kg$) enters a 0.5 T magnetic field perpendicularly at $2 \times 10^5 m/s$. Calculate the radius of its circular path.
Step 1: Identify Formula. Centripetal force is provided by the Magnetic Force.
$$\frac{mv^2}{r} = qvB \implies r = \frac{mv}{qB}$$
Step 2: Plug in values.
$$r = \frac{(1.67 \times 10^{-27})(2 \times 10^5)}{(1.6 \times 10^{-19})(0.5)}$$
Step 3: Calculate.
$$r = \frac{3.34 \times 10^{-22}}{8.0 \times 10^{-20}} = 0.4175 \times 10^{-2} \text{ m} \approx 4.18 \text{ mm}$$
Problem 2: Faraday's Law
A 50-turn coil of area $0.1 m^2$ is placed perpendicular to a magnetic field. The field strength drops from 1.0 T to 0 T in 0.2 seconds. What is the average induced EMF?
Step 1: Calculate Flux Change ($\Delta \Phi$).
$$\Delta \Phi = A(B_{final} - B_{initial}) = 0.1(0 - 1.0) = -0.1 \text{ Wb}$$
Step 2: Use Faraday's Law.
$$\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}$$
$$\mathcal{E} = -50 \left(\frac{-0.1}{0.2}\right) = -50 (-0.5) = +25 \text{ V}$$
Problem 3: Magnetic Force on a Wire
A straight wire of length 2.0 m carries a current of 5.0 A. It is placed in a uniform magnetic field of 0.3 T at an angle of 30° to the field. Calculate the magnetic force on the wire.
Step 1: Identify Formula.
$$F = I L B \sin\theta$$
Step 2: Plug in values.
$$F = (5.0)(2.0)(0.3)\sin(30^\circ) = 3.0 \times 0.5 = 1.5 \text{ N}$$
Problem 4: Transformer Equation
An ideal transformer has 200 turns on the primary coil and 800 turns on the secondary coil. If the primary voltage is 120 V AC, what is the secondary voltage?
Step 1: Identify Formula.
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
Step 2: Rearrange and Solve.
$$V_s = V_p \times \frac{N_s}{N_p} = 120 \times \frac{800}{200} = 120 \times 4 = 480 \text{ V}$$
Part 7: Advanced Toolkit - Graphical Analysis (No Calculus)
You don't need complex calculus to solve advanced physics problems. You can understand the relationships between physical quantities purely through Slopes and Areas under graphs.
7.1 Kinematics: The Ladder of Motion
Slopes (Rates of Change)
To go from Position $\to$ Velocity $\to$ Acceleration, we look at the slope ($\Delta y / \Delta x$) of the graph.
- Velocity ($v$): Slope of the Position-Time ($x-t$) graph. ($v = \frac{\Delta x}{\Delta t}$)
- Acceleration ($a$): Slope of the Velocity-Time ($v-t$) graph. ($a = \frac{\Delta v}{\Delta t}$)
Areas Under the Curve
To go "backwards" (Acceleration $\to$ Velocity $\to$ Position), we calculate the area under the graph.
- Change in Velocity ($\Delta v$): Area under the Acceleration-Time ($a-t$) graph.
- Displacement ($\Delta x$): Area under the Velocity-Time ($v-t$) graph.
7.2 Work with Variable Forces
The standard formula $W = Fd$ only works if the force is constant. If the force changes (like stretching a spring), you cannot just multiply. Instead, Work is the Area under the Force vs. Distance graph.
Example: Spring Potential Energy
Hooke's Law states the force needed to stretch a spring is $F = kx$. If we graph this, it forms a straight line starting from the origin. The area under this line forms a triangle.
$$\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$$
$$W = \frac{1}{2} \times (x) \times (kx) = \frac{1}{2}kx^2$$
By simply calculating the area of the triangle, we derived the formula for elastic potential energy without any complex math!
7.3 Impulse & Momentum
Newton's Second Law relates force and time to changes in momentum. Impulse ($J$) is the total change in momentum ($\Delta p$).
Graphically, Impulse is the Area under a Force-Time ($F-t$) graph. This perfectly explains why car airbags work: they increase the collision time ($\Delta t$), which flattens the graph. The area (total change in momentum) stays the same, but the peak Force ($F$) is drastically reduced, saving the passenger.