# Gate 2016 EE – Set 2 – Question 55

Given l=1m, V=1V, B=1T

Voltage induced is given by the formula, $$\int_{0}^{1}E_{m}\cdot dl$$, where $$E_{m}$$ is the induced electric field.

Voltage induced = $$E_{m} volts = 1V/m$$

$$E_{m}=\bar{v}\times \bar{B}$$

Where, $$v = radius of path \times angular velocity$$

$$1V/m = v \times 1 Tesla$$

v = 1m/sec

$$v = r \times \omega m/s$$

Since r = 1m, then, $$\omega =1rad/sec$$

We know the formula for speed as, $$N = \frac{60\omega }{2\pi }=\frac{60\times 1}{2\times 3.14}=9.55rev/min$$