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Q.

A rod of length 10 cm made up of conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with constant angular velocity 10 rad/s about point O, in a constant magnetic field 2T as shown in the figure. The induced emf between the point A and B of rod will be

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a

0.051 V

b

0.1 V

c

0.029 V

d

0.064 V

answer is C.

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Detailed Solution

$x_{2} = 0.10 m$

The emf induced between the point A and B of rod,

$\begin{array}{rcl} e & = & \int_{x_{1} = 0.07}^{x_{2} = 0.10} B (ω x) d x \\ = & ω B \int_{0.07}^{0.1} x d x = ω B {[\frac{x^{2}}{2}]}_{0.07}^{0.1} \\ = & 2 \times 10 \times [\frac{{(0.1)}^{2}}{2} - \frac{{(0.07)}^{2}}{2}] \\ = & 0.05092 \approx 0.051 \end{array}$

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