A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev / min in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is 0.4 G, the induced e.m.f between the axle and the rim of the wheel equal to

Question

A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev / min in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is 0.4 G, the induced e.m.f between the axle and the rim of the wheel equal to (A) 1.256 × 10-3 V (B) 6.28 × 10-4 V (C) 1.256 × 10-4 V (D) 6.28 × 10-5 V

Tardigrade Admin · Accepted Answer

e=(1/2) B ω l2 =(1/2) × 0.4 × 10-4 × 2 π × (120/60) × (1/4) =2 × 3.14 × 10-5 =6.28 × 10-5 V

Q. A wheel with $10$ metallic spokes each $0.5 m$ long is rotated with a speed of $120 re v / min$ in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is $0.4 G$ , the induced e.m.f between the axle and the rim of the wheel equal to

$1.256 \times 1 0^{- 3} V$

$6.28 \times 1 0^{- 4} V$

$1.256 \times 1 0^{- 4} V$

$6.28 \times 1 0^{- 5} V$

$e = \frac{1}{2} B ω l^{2}$
$= \frac{1}{2} \times 0.4 \times 1 0^{- 4} \times 2 π \times \frac{120}{60} \times \frac{1}{4}$
$= 2 \times 3.14 \times 1 0^{- 5}$
$= 6.28 \times 1 0^{- 5} V$

Q. A wheel with 10 metallic spokes each 0.5m long is rotated with a speed of 120rev/min in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is 0.4G, the induced e.m.f between the axle and the rim of the wheel equal to

1.256×10−3V

6.28×10−4V

1.256×10−4V

6.28×10−5V