1.Easy
A rectangular loop of 12 cm by 25 cm lies in a uniform magnetic field of 0.4 T. The field lines make an angle of 53° with the plane of the loop. Find the magnetic flux Φ through the loop.
B = 0.4 TA = 12 cm × 25 cm53° to the plane
Φ = mWb
Magnetic fields & induction worksheet with answers
2.Easy
An electron moves at 6 × 10⁶ m/s perpendicular to a uniform magnetic field of 1.5 T. Find the magnitude of the magnetic force F on it.
|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁶ m/sB = 1.5 Tθ = 90°
F = pN
3.Medium
A coil of 50 turns has an area of 100 cm². The coil sits in a uniform field of 0.5 T perpendicular to its plane, and the field is switched off in 50 ms. Find the average induced emf ε.
N = 50A = 100 cm²B = 0.5 TΔt = 50 ms
ε = V
4.Medium
A square loop moves to the right into a region with a uniform magnetic field pointing out of the page. Click the direction of the induced current in the loop as seen in the drawing, while the loop is entering the field.
B: out of the pageentering the field
- 1clockwise
- 2counterclockwise
5.Hard
A proton starts from rest, is accelerated through a potential difference of 5000 V and then enters a uniform magnetic field of 0.25 T at right angles. Find the radius r of its path in the field.
m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 5000 VB = 0.25 T
r = cm
6.Hard
A short coil of 20 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 20 cm and diameter 2 cm. Find their mutual inductance M.
N1 = 1500N2 = 20l = 20 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A
M = µH
Answer key
- 1. Φ = 9.584 mWb
- 2. F = 1.442 pN
- 3. ε = 5 V
- 4. clockwise
- 5. r = 4.088 cm
- 6. M = 59.22 µH
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