IB DP Physics: HL复习笔记5.4.4 Solving Problems Involving Magnetic Forces

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

  1. Explain whether the speed of the proton is the same when entering and exiting the magnetic field.
  2. 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
Part (b)
Step 1: List the known quantities
  • Magnetic field strength, B = 0.3 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
Step 5: State final answer
R = 1.63 × 10−2 m = 1.63 cm in a circular motion
转载自savemyexams
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