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IB DP Physics: HL復習筆記5.4.4 Solving Problems Involving Magnetic Forces

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年8月1日下午12:42

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:

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

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 0.3 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