1.Easy
A rectangular loop of 5 cm by 15 cm lies in a uniform magnetic field of 0.6 T. The field lines make an angle of 20° with the plane of the loop. Find the magnetic flux Φ through the loop.
B = 0.6 TA = 5 cm × 15 cm20° to the plane
Φ = mWb
Magnetic fields & induction worksheet with answers
2.Easy
A flat circular coil of 25 turns and radius 15 cm carries a current of 4 A. Find the magnetic flux density B at its centre.
N = 25I = 4 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
A coil of 50 turns has an area of 10 cm². The coil sits in a uniform field of 0.4 T perpendicular to its plane, and the field is switched off in 100 ms. Find the average induced emf ε.
N = 50A = 10 cm²B = 0.4 TΔt = 100 ms
ε = mV
4.Medium
A coil of 500 turns has an area of 80 cm². The coil sits in a uniform field of 0.2 T perpendicular to its plane, and the field is switched off in 20 ms. Find the average induced emf ε.
N = 500A = 80 cm²B = 0.2 TΔt = 20 ms
ε = V
5.Hard
A deuteron starts from rest, is accelerated through a potential difference of 2500 V and then enters a uniform magnetic field of 0.5 T at right angles. Find the radius r of its path in the field.
m = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 2500 VB = 0.5 T
r = cm
6.Hard
A long air-core solenoid has 1000 turns, a length of 50 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 1.5 A.
N = 1000l = 50 cm⌀ = 2.5 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = mJ
Answer key
- 1. Φ = 1.539 mWb
- 2. B = 418.9 µT
- 3. ε = 200 mV
- 4. ε = 40 V
- 5. r = 2.043 cm
- 6. W = 1.388 mJ
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