Quick answer: A magnetic field exerts a force on moving charges and on current-carrying wires. This Physics 11-12 worksheet on magnetic fields gives 20 problems from easy to hard: force on a lab wire, direction of the force and electron in a field. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train you to apply F = BIL and F = Bqv, to find the direction of magnetic forces, and to analyse circular motion of charged particles. They move from one-step substitutions to velocity selectors, cyclotrons and mass spectrometers.
They suit A Level, IB Physics, CBSE Class 12 and WAEC senior students. Use e = 1.60 × 10⁻¹⁹ C, electron mass 9.11 × 10⁻³¹ kg and proton mass 1.67 × 10⁻²⁷ kg.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.3
Problem 1 Force on a lab wire ★★★
Aarav in Pune hangs a 0.50 m wire between the poles of a magnet. The field is 0.40 T and the wire carries 3.0 A at right angles to it.1. Calculate the force on the wire.
Problem 2 Direction of the force ★★★
A wire carries current due north through a field that points vertically downwards. Take east, north and up as a right-handed set.1. State the direction of the force on the wire.
2. State the direction if the current is reversed.
Problem 3 Electron in a field ★★★
Chiamaka in Lagos fires electrons at 5.0 × 10⁶ m/s at right angles into a 0.20 T field.1. Calculate the force on each electron.
Problem 4 Finding the field ★★★
A 0.15 m wire carrying 6.0 A at right angles to a uniform field feels a force of 0.054 N.1. Calculate the flux density.
Problem 5 Wire at an angle ★★★
A 0.40 m wire carrying 2.0 A lies at 30° to a field of 0.25 T.1. Calculate the force on the wire.
2. State the force when the wire is turned parallel to the field.
Problem 6 Power cable and Earth’s field ★★★
Kofi in Accra studies a horizontal cable 80 m long carrying 250 A. Earth’s field there is 45 µT and is perpendicular to the cable.1. Convert 45 µT to tesla.
2. Calculate the force on the cable.
Problem 7 Speed unchanged ★★★
A proton moves in a circle in a uniform magnetic field.1. Explain why its speed stays constant.
2. State what happens to its kinetic energy.
Problem 8 Proton orbit radius ★★★
A proton enters a 0.80 T field at 4.0 × 10⁶ m/s, perpendicular to the field.1. Calculate the radius of its circular path in cm.
Problem 9 Cyclotron frequency of an electron ★★★
Mei in Singapore models an electron in a 1.5 mT field.1. Calculate the time for one complete circle.
2. Calculate the frequency of the motion.
3. State how the answers change if the speed is doubled.
Problem 10 Selecting a speed ★★★
A velocity selector has an electric field of 2.4 × 10⁴ V/m and a magnetic field of 0.080 T.1. Calculate the speed of particles that pass straight through.
2. Explain what happens to a faster particle of the same charge.
Problem 11 Electron gun then field ★★★
An electron is accelerated from rest through 150 V and then enters a 1.0 mT field at right angles.1. Calculate its speed after acceleration.
2. Calculate the radius of its path in the field.
Problem 12 Floating wire ★★★
Diego in Texas balances a horizontal wire of mass per unit length 4.0 × 10⁻³ kg/m in a horizontal field of 0.050 T, perpendicular to the wire, using g = 9.81 N/kg.2. Calculate the current needed.
Problem 13 Reading a force graph ★★★
The graph shows the force on a 0.25 m wire for different currents in a uniform field.1. Find the gradient of the line of best fit.
2. Use it to calculate the flux density.
3. Explain why the line passes through the origin.
Problem 14 Proton against alpha particle ★★★
A proton and an alpha particle (mass 6.64 × 10⁻²⁷ kg, charge +2e) enter the same field at the same speed, at right angles to it.1. Calculate the ratio of the radius of the alpha path to that of the proton.
2. Explain the result in terms of mass and charge.
Problem 15 Tracks in a bubble chamber ★★★
Two particles with charges of equal size enter a field pointing into the page at the same point, travelling to the right. The tracks are shown.2. State which particle has the greater momentum.
3. Explain why both tracks are arcs of circles.
Problem 16 Proton cyclotron ★★★
The largest circle in a cyclotron has a radius of 0.45 m in a 1.2 T field. Protons leave on this circle.1. Calculate their speed.
2. Calculate their kinetic energy in joules.
3. Convert the energy to MeV (1 eV = 1.60 × 10⁻¹⁹ J).
Problem 17 Spiral path ★★★
An electron enters a 2.0 mT field with speed 4.0 × 10⁶ m/s at 60° to the field lines.1. Resolve its velocity into components perpendicular and parallel to B.
2. Calculate the radius of the circular part of the motion.
3. Calculate the distance advanced along the field in one turn (the pitch).
Problem 18 Coil in a field ★★★
A rectangular coil of 40 turns has two vertical sides 5.0 cm long, 3.0 cm apart, in a horizontal field of 0.15 T parallel to the plane of the coil. The current is 0.80 A.1. Calculate the force on one vertical side.
2. State the direction of the force on the other vertical side.
3. Calculate the turning moment (couple) on the coil.
Problem 19 Separating chlorine ions ★★★
Singly charged chlorine ions of mass 35 u and 37 u are accelerated through 2.0 kV and then travel in a semicircle in a 0.50 T field (1 u = 1.66 × 10⁻²⁷ kg).1. Show that r = (1/B)√(2mV/q).
2. Calculate the two radii.
3. Calculate the distance between the landing points.
Problem 20 Checking a student’s solution ★★★
A student writes: “A proton at 2.0 × 10⁶ m/s in a 0.40 T field has r = mv/(qB) = 0.52 m and a period of 1.6 × 10⁻⁶ s.”1. Show that the radius is wrong and give the correct value.
2. Calculate the correct period.
3. Suggest a quick estimate that would have exposed the error.
