Solving Problems Involving Magnetic Forces

There is a lot of mathematics surrounding magnetism and magnetic forces
The key equations are:

Force on a current-carrying conductor:
F = BIL

Force on a moving charge:
F = Bqv

Radius of a moving charge in a magnetic field:
r =

\frac{m v}{q B}

Below are two worked examples demonstrating different situations involving magnetic forces

Worked example

A 5 cm length of wire is at 90° to the direction of an external magnetic field. When a current of 1.5 A flows through the wire it experiences a force of 0.06 N from the motor effect.

Calculate the magnetic flux density of the magnet.

Step 1: List the known quantities

Length, L = 5 cm = 0.05 m
Current, I = 1.5 A
Force, F = 0.06 N

Step 2: Write out the equation for magnetic force

F = BIL

Step 3: Rearrange the equation to make B the subject

B = \frac{F}{I L}

Step 4: Substitute values into the equation

$B = \frac{0.06}{1.5 \times 0.05} = 0.8 T$

Worked example

This question is about the movement of an electrically charged particle into a magnetic field. An electron enters a magnetic field and moves in an approximately circular path as shown below.

5-4-4-electron-movement-we2_sl-physics-rn

Explain whether the speed of the proton is the same when entering and exiting the magnetic field.
The magnetic field has a strength of 0.003 T and the velocity of the electron before entering the magnetic field is 8.6 × 10⁶ m s⁻¹ to the left. Show that the radius of the motion of the electrons is 1.63 cm.

Part (a)

- The answer is that the work done by the magnetic force on the charge must be zero
- This is because the force itself is at right angles to the velocity
- Since the work done is zero, therefore the kinetic energy does not change between entering and leaving the magnetic field
- Therefore the speed is the same

Part (b)

Step 1: List the known quantities

Magnetic field strength, B = 0.003 T
Velocity of electron (before entering field), v = 8.6 × 10⁶ m s⁻¹ to the left
Radius of motion to be shown, r = 1.63 cm

Step 2: Equate the magnetic force and the force of circular motion

This can be done for the situation since the circular motion is caused by the magnetic force

q v B = \frac{m v^{2}}{r}

Step 3: Rearrange the equation to find the radius

qvBr = mv²
qBr = mv

r = \frac{m v}{q B}

Step 4: Substitute in the values

r = \frac{(9.1 \times 10^{- 31}) \times (8.6 \times 10^{6})}{(1.6 \times 10^{- 19}) \times (3 \times 10^{- 3})} = 1.63 \times 10^{- 2} m

Step 5: State final answer

R = 1.63 × 10⁻² m = 1.63 cm in a circular motion

Solving Problems Involving Magnetic Forces (DP IB Physics: HL)

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1. Measurement & Uncertainties

1.1 Measurements in Physics

1.1.1 SI Units

1.1.2 Using Scientific Notation

1.1.3 Estimating Physical Quantities

1.2 Uncertainties & Errors

1.2.1 Random & Systematic Errors

1.2.2 Calculating Uncertainties

1.2.3 Determining Uncertainties from Graphs

1.3 Vectors & Scalars

1.3.1 Vector & Scalar Quantities

1.3.2 Combining & Resolving Vectors

1.3.3 Solving Vector Problems

2. Mechanics

2.1 Motion

2.1.1 Distance & Displacement

2.1.2 Speed & Velocity

2.1.3 Acceleration

2.1.4 Graphs Describing Motion

2.1.5 Uniform Acceleration

2.1.6 Acceleration of Free Fall Experiment

2.1.7 Projectile Motion

2.1.8 Terminal Speed

2.2 Forces

2.2.1 Free-Body Diagrams

2.2.2 Newton’s First Law

2.2.3 Newton’s Second Law

2.2.4 Newton’s Third Law

2.2.5 Applying Newton’s Laws of Motion

2.2.6 Friction

2.3 Work, Energy & Power

2.3.1 Kinetic Energy

2.3.2 Gravitational Potential Energy

2.3.3 Elastic Potential Energy

2.3.4 Work Done

2.3.5 Power

2.3.6 Principle of Conservation of Energy

2.3.7 Efficiency

2.4 Momentum & Impulse

2.4.1 Force & Momentum

2.4.2 Impulse

2.4.3 Conservation of Linear Momentum

2.4.4 Collisions & Explosions

3. Thermal Physics

3.1 Thermal Concepts

3.1.1 Solids, Liquids & Gases

3.1.2 Temperature

3.1.3 Internal Energy

3.1.4 Specific Heat Capacity

3.1.5 Specific Latent Heat

3.1.6 Phase Change

3.1.7 Investigating Thermal Energy

3.2 Modelling a Gas

3.2.1 Ideal Gas Laws

3.2.2 Ideal Gas Equation

3.2.3 Kinetic Model of an Ideal Gas

3.2.4 Mole Calculations

3.2.5 Investigating Gas Laws

4. Waves

4.1 Oscillations

4.1.1 Properties of Oscillations

4.1.2 Simple Harmonic Oscillations

4.1.3 SHM Graphs

4.1.4 Energy in SHM

4.2 Travelling Waves

4.2.1 Properties of Waves

4.2.2 Transverse & Longitudinal Waves

4.2.3 Electromagnetic Waves

4.2.4 Sound Waves

4.3 Wave Characteristics

4.3.1 Wavefronts

4.3.2 Amplitude & Intensity

4.3.3 Superposition

4.3.4 Polarisation

4.3.5 Malus’s Law