IB Physics SL D.3 Motion in electromagnetic fields questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

Type

Multiple choice Written

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Question 1

Multiple choiceMedium1 mark

Particles X and Y, each with charge magnitude $q$ enter the same uniform magnetic field at right angles to the field with equal speeds. Only magnetic forces act. Each follows a semicircular path, and Y’s path radius is twice X’s. Which row gives the ratios $(|q|/m)_Y/(|q|/m)_X$ and $K_Y/K_X$ respectively, after both particles complete their semicircles?

Show answer and explanation

Answer: B. The magnetic force supplies the centripetal force, so $|q|vB=mv^2/r$ giving $|q|/m=v/(Br)$ With equal speeds and the same field, the charge-to-mass ratio is inversely proportional to radius, so the ratio for Y and X is $1/2$ Equal charge magnitudes then give $m_Y/m_X=2$ and equal speeds give $K_Y/K_X=2$ The magnetic force is perpendicular to the motion, so neither particle’s kinetic energy changes during its semicircle.

A: Gets the charge-to-mass ratio right but assumes equal speeds mean equal kinetic energies, overlooking the different masses.
C: Treats charge-to-mass ratio as directly proportional to radius; this also gives the inverse mass and kinetic-energy ratio.
D: Reverses the charge-to-mass ratio’s dependence on radius but correctly uses $K\propto m$ at equal speed.
Remember: a magnetic force changes a particle’s direction, not its kinetic energy.

Question 2

Paper 2Medium8 marks

An electron enters the region between two parallel plates as shown in Figure 1. The electric field between the plates is uniform. Ignore edge effects and the gravitational force on the electron. The electron has no initial vertical velocity.

The magnitude of the electron’s charge is $1.60\times10^{-19}\ \mathrm{C}$ and its mass is $9.11\times10^{-31}\ \mathrm{kg}$

(a)

State the direction of the electric force on the electron.

[1]

(b)

Calculate the magnitude of the electric field between the plates.

[1]

(c)

Calculate the magnitude of the electron’s acceleration between the plates.

[2]

(d)

Determine the vertical displacement of the electron from its entry point when it reaches the right end of the plates.

[3]

(e)

Determine the vertical component of the electron’s velocity at the instant it reaches the right end of the plates.

[1]

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