Charged particle in a magnetic field: Class 12 practice
A charge moving perpendicular to a magnetic field moves in a circle: r = mv/(qB). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Magnetic force
The idea behind charged particle in a magnetic field
A charge moving perpendicular to a magnetic field moves in a circle: r = mv/(qB). Its period T = 2πm/(qB) does not depend on speed — the basis of the cyclotron frequency f = qB/(2πm).
Step-by-step method
- Use r = mv/(qB).
- Period T = 2πm/(qB).
- Frequency f = 1/T.
Worked example 1 (Basic)
A alpha particle moves at 1e+5 m/s perpendicular to a 1.5 T field. Find the radius of its path.
- r = mv/(qB)
- = 1.383e-3 m
- Answer: 1.383e-3 m
Worked example 2 (Standard)
A alpha particle moves at 7e+6 m/s perpendicular to a 1.3 T field. Find the radius of its path.
- r = mv/(qB)
- = 1.117e-1 m
- Answer: 1.117e-1 m
Worked example 3 (Challenge)
Find the cyclotron frequency of a electron in a 0.6 T field.
- f = qB/(2πm)
- = 1.677e+10 Hz
- Answer: 1.677e+10 Hz
Common mistakes and misconceptions
- Thinking the period depends on speed
- Using the wrong charge for an alpha particle
Practice questions
- (Basic) A electron moves at 7e+5 m/s perpendicular to a 0.4 T field. Find the radius of its path.
- (Basic) A proton moves at 9e+6 m/s perpendicular to a 1.2 T field. Find the radius of its path.
- (Standard) A alpha particle moves at 1e+6 m/s perpendicular to a 0.4 T field. Find the radius of its path.
- (Standard) A alpha particle moves at 2e+5 m/s perpendicular to a 0.9 T field. Find the radius of its path.
- (Challenge) Find the cyclotron frequency of a proton in a 1.2 T field.
- (Challenge) Find the cyclotron frequency of a proton in a 0.3 T field.
Answer key with full working
- Q1: r = mv/(qB) → = 9.964e-6 m → Answer: 9.964e-6 m
- Q2: r = mv/(qB) → = 7.828e-2 m → Answer: 7.828e-2 m
- Q3: r = mv/(qB) → = 5.188e-2 m → Answer: 5.188e-2 m
- Q4: r = mv/(qB) → = 4.611e-3 m → Answer: 4.611e-3 m
- Q5: f = qB/(2πm) → = 1.830e+7 Hz → Answer: 1.830e+7 Hz
- Q6: f = qB/(2πm) → = 4.575e+6 Hz → Answer: 4.575e+6 Hz
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 charged particle in a magnetic field 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.