Magnetic force and circular paths: Class 12 practice
F = qvB sin θ on a moving charge and F = BIL sin θ on a current. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Circular motion
The idea behind magnetic force and circular paths
F = qvB sin θ on a moving charge and F = BIL sin θ on a current. A charge moving perpendicular to B goes in a circle of radius r = mv/(qB) with period T = 2πm/(qB).
Step-by-step method
- Find the angle between v (or I) and B.
- Use F = qvB sin θ or BIL sin θ.
- For circles: r = mv/qB.
Worked example 1 (Basic)
A 0.9 m wire carrying 9 A is at 90° to a 0.1 T field. Find the force.
- F = BIL sin θ
- = 0.81 N
- Answer: 0.81 N
Worked example 2 (Standard)
An electron moves at 5e+6 m/s perpendicular to a 3 mT field. Find the radius of its path.
- r = mv/qB
- = 9.479e-3 m
- Answer: 9.479e-3 m
Worked example 3 (Challenge)
Find the period of an electron circling in a 3 mT field.
- T = 2πm/qB
- = 1.191e-8 s (independent of speed)
- Answer: 1.191e-8 s
Common mistakes and misconceptions
- Forgetting sin θ
- Thinking the magnetic force changes speed
Practice questions
- (Basic) A 0.1 m wire carrying 2 A is at 90° to a 0.4 T field. Find the force.
- (Basic) A 0.3 m wire carrying 2 A is at 30° to a 0.3 T field. Find the force.
- (Standard) An electron moves at 2e+6 m/s perpendicular to a 2 mT field. Find the radius of its path.
- (Standard) An electron moves at 6e+6 m/s perpendicular to a 6 mT field. Find the radius of its path.
- (Challenge) Find the period of an electron circling in a 6 mT field.
- (Challenge) Find the period of an electron circling in a 5 mT field.
Answer key with full working
- Q1: F = BIL sin θ → = 0.08 N → Answer: 0.08 N
- Q2: F = BIL sin θ → = 0.09 N → Answer: 0.09 N
- Q3: r = mv/qB → = 5.687e-3 m → Answer: 5.687e-3 m
- Q4: r = mv/qB → = 5.687e-3 m → Answer: 5.687e-3 m
- Q5: T = 2πm/qB → = 5.956e-9 s (independent of speed) → Answer: 5.956e-9 s
- Q6: T = 2πm/qB → = 7.147e-9 s (independent of speed) → Answer: 7.147e-9 s
Syllabus note
This skill is listed under "Moving Charges and Magnetism" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is magnetic force and circular paths in?
"Moving Charges and Magnetism", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.