1.Easy
A rectangular loop of 20 cm by 15 cm lies in a uniform magnetic field of 1.2 T. The field makes an angle of 20° with the normal of the loop. Find the magnetic flux Φ through the loop.
B = 1.2 TA = 20 cm × 15 cm20° to the normal
Φ = mWb
Magnetic fields & induction worksheet with answers
2.Easy
A long straight wire carries a current of 4 A. Find the magnetic flux density B at point P, 2.5 cm from the wire.
I = 4 Ar = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
An alpha particle moves at 2.5 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.4 T. Find the radius r of its circular path.
m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 2.5 × 10⁵ m/sB = 0.4 T
r = cm
4.Medium
A metal rod 40 cm long slides at 2 m/s along two rails in a uniform field of 0.6 T into the page. The rails are joined by a resistor of 5 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).
B = 0.6 TL = 40 cmv = 2 m/sR = 5 Ω
F = mN
5.Hard
A long air-core solenoid has 1000 turns, a length of 20 cm and a diameter of 4 cm. Find its self-inductance L.
N = 1000l = 20 cm⌀ = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = mH
6.Hard
A short coil of 200 turns is wound tightly round the middle of a long solenoid of 1000 turns, length 50 cm and diameter 2 cm. The current in the solenoid changes at 200 A/s. Find the emf ε induced in the short coil.
N1 = 1000N2 = 200l = 50 cm⌀ = 2 cmdi/dt = 200 A/sμ₀ = 4π × 10⁻⁷ T·m/A
ε = mV
Answer key
- 1. Φ = 33.83 mWb
- 2. B = 32 µT
- 3. r = 1.296 cm
- 4. F = 23.04 mN
- 5. L = 7.896 mH
- 6. ε = 31.58 mV
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