A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 ms -1, at right angles to the horizontal component of the earth's magnetic field of strength 0.30 × 10-4 Wbm -2. The instantaneous value of the induced potential gradient in the wire from west to east is

Question

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 ms -1, at right angles to the horizontal component of the earth's magnetic field of strength 0.30 × 10-4 Wbm -2. The instantaneous value of the induced potential gradient in the wire from west to east is (A) +1.5 × 10-3 Vm -1 (B) -1.5 × 10-3 Vm -1 (C) +1.5 × 10-4 Vm -1 (D) -1.5 × 10-4 Vm -1

Tardigrade Admin · Accepted Answer

Given, B=0.30 × 10-4 Wb m -2, v=5 ms -1 and l=10 m <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/338c8c3ee9c94b2a06ae9757aa5a5a7a-.png" /> As induced emf or potential, e=B v l So, induced potential gradient =(e/l)=B v =0.3 × 10-4 × 5=1.5 × 10-4 Vm -1 Here, East end B at positive potential gradient means increasing potential.

$+ 1.5 \times 1 0^{- 3} V m^{- 1}$

$- 1.5 \times 1 0^{- 3} V m^{- 1}$

$+ 1.5 \times 1 0^{- 4} V m^{- 1}$

$- 1.5 \times 1 0^{- 4} V m^{- 1}$

+1.5×10−3Vm−1

−1.5×10−3Vm−1

+1.5×10−4Vm−1

−1.5×10−4Vm−1

Given, B=0.30×10−4Wbm−2,v=5ms−1 and l=10m As induced emf or potential, e=Bvl So, induced potential gradient =le​=Bv =0.3×10−4×5=1.5×10−4Vm−1 Here, East end B at positive potential gradient means increasing potential.

$+ 1.5 \times 1 0^{- 3} V m^{- 1}$

$- 1.5 \times 1 0^{- 3} V m^{- 1}$

$+ 1.5 \times 1 0^{- 4} V m^{- 1}$

$- 1.5 \times 1 0^{- 4} V m^{- 1}$