Question

a conductor of length 3cm moving in a uniform magnetic field of strength 100th. It covers a distance of 70m in 5 sec. It's plane of motion makes an angle of 30° with the direction of magnetic field. Calculate the emf induced in it​

Answer 1

Answer: The induced emf in the conductor is 21 weber.

Explanation

Given that,

Length l = 3 cm

Strength of magnetic field B = 100 T

Distance d = 70 m

Time t = 5 sec

Angle $\theta = 30^{0}$

We know that,

Speed = distance /time

$v = \dfrac{d}{t}$

$v = \dfrac{70}{5}$

$v = 14 m/s$

Now, the induced e.m.f is

$e = \dfrac{d\phi}{dt} = \dfrac{BdA}{dt} = \dfrac{Blvdt}{dt}$

The induced e.m.f with an angle is

$e = Blvsin\ \theta$

$e = 100\T\times3\times10^{-2}m\times14\ m\times sin30^{0}$

$e = 100\T\times3\times10^{-2}m\times14\ m\times\dfrac{1}{2}$

$e =21 Wb$

Hence, The induced emf in the conductor is 21 weber.