1.Easy
A rectangular loop of 12 cm by 30 cm lies in a uniform magnetic field of 0.8 T. The field lines make an angle of 45° with the plane of the loop. Find the magnetic flux Φ through the loop.
B = 0.8 TA = 12 cm × 30 cm45° to the plane
Φ = mWb
Magnetic fields & induction worksheet with answers
2.Easy
A rectangular loop of 5 cm by 25 cm lies in a uniform magnetic field of 0.1 T. The field makes an angle of 0° with the normal of the loop. Find the magnetic flux Φ through the loop.
B = 0.1 TA = 5 cm × 25 cm0° to the normal
Φ = mWb
3.Medium
A metal rod 20 cm long slides at 1 m/s along two rails in a uniform field of 0.2 T into the page. Find the induced emf ε between its ends.
B = 0.2 TL = 20 cmv = 1 m/s
ε = mV
4.Medium
A coil of 250 turns has an area of 50 cm². A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.15 T in 10 ms. Find the average induced emf ε.
N = 250A = 50 cm²B: 0.05 T → 0.15 TΔt = 10 ms
ε = V
5.Hard
A proton starts from rest, is accelerated through a potential difference of 500 V and then enters a uniform magnetic field of 0.4 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 = 500 VB = 0.4 T
r = cm
6.Hard
A long air-core solenoid has 2000 turns, a length of 20 cm and a diameter of 2 cm. Find its self-inductance L.
N = 2000l = 20 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = mH
Answer key
- 1. Φ = 20.36 mWb
- 2. Φ = 1.25 mWb
- 3. ε = 40 mV
- 4. ε = 12.5 V
- 5. r = 0.8079 cm
- 6. L = 7.896 mH
Full step-by-step solutions: practise this topic on examproblems.com.