Electromagnetic forces: currents, fields and beams
Key idea: Keep field production, conductor force and moving-charge force distinct, apply direction rules with charge sign, and compare electric and magnetic beam deflection before balancing crossed fields.
Before you start: Current Electricity objective chainD.C. Circuits objective chainElectric Fields objective chain
By the end, you can
- Represent and calculate magnetic fields produced by straight wires, flat coils and long solenoids.
- Analyse conductor forces, define flux density, use a current balance and predict parallel-current interactions.
- Calculate and direct magnetic force on moving positive or negative charges.
- Compare charged-beam deflection in uniform electric and magnetic fields.
- Explain and calculate crossed-field velocity selection.
Starting-point self-check
1. Check your starting point
Attempt all five groups without notes and mark the first geometry, direction, force, trajectory or balance decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Force on a moving charge 17(j)–(k)
Question 1
An electron travels at 2.0 × 10⁶ m s⁻¹ perpendicular to a 0.25 T field into the page. Find force magnitude and initial direction if velocity is right.
Check the model response
F = B|Q|v = 8.0 × 10⁻¹⁴ N. A positive charge would be forced upward; the electron's force is downward.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Force on a moving charge 17(j)–(k)
Check this idea
Misconception: A negative charge follows the positive-charge force direction.
Repair: Determine v × B for positive charge, then reverse the direction for negative charge.
Check this idea
Misconception: The full speed contributes when velocity is oblique to B.
Repair: Only v sin θ, the component perpendicular to B, contributes to magnetic force.
worked example
3. Follow five worked models
Follow how each solution fixes source geometry, conventional direction, charge sign, field uniformity or force opposition before calculating.
Force on a moving charge 17(j)–(k)
Model 1
A proton enters a 0.40 T field at 30° to the field with speed 5.0 × 10⁶ m s⁻¹. Find magnetic force.
Check the model response
F = BQv sin θ = (0.40)(1.60 × 10⁻¹⁹)(5.0 × 10⁶)sin30° = 1.60 × 10⁻¹³ N. Only the velocity component perpendicular to B contributes.
guided practice
4. Guided practice
Use each hint only to select the correct geometry, sine component, direction rule or force balance.
Force on a moving charge 17(j)–(k)
Question 1
A charge moves exactly parallel to a magnetic field. Find its magnetic force.
Hint: Only perpendicular velocity produces magnetic force.
Check the model response
F = BQv sin0° = 0.
independent practice
5. Independent practice
Solve without repair notes and state every long-wire, flat-coil, long-solenoid, uniform-field and perpendicular-motion assumption.
Force on a moving charge 17(j)–(k)
Question 1
Give a reliable direction method for positive and negative charges and explain why magnetic force does no work.
Check the model response
First determine v × B for a positive charge using a right-hand vector rule, then reverse for negative charge. The force is perpendicular to instantaneous velocity, so F·v = 0 and kinetic energy remains constant.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Force on a moving charge 17(j)–(k)
Question 1
A +3.2 × 10⁻¹⁹ C ion travels at 4.0 × 10⁵ m s⁻¹ at 60° to 0.50 T. Find force magnitude and state its relation to v and B.
Check the model response
F = BQv sin60° = 5.54 × 10⁻¹⁴ N. It is perpendicular to both the velocity component and B, with direction from Q(v × B).
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Force on a moving charge 17(j)–(k)
Question 1
A negative charge reverses its velocity in the same B. Compare the new force direction with the original.
Check the model response
Reversing v reverses v × B. The negative charge already reverses the positive-charge direction, so the new force is opposite to the original force on that same negative charge.