Ncert Exercises & Solutions

Q 5. We are rotating a 1 m long metallic rod with an angular frequency of 400 red $s - 1 <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>$ with an axis normal to the rod passing through its one end. And on to the other end of the rod, it is connected with a circular metallic ring. There exist a uniform magnetic field of 0.5 T which is parallel to the axis everywhere. Find out the emf induced between the center and the ring.

Length of the rod = 1m

Angular frequency, $ω = 400 r a d / s$

Magnetic field strength, B = 0.5 T

At one of the ends of the rod, it has zero liner velocity, while on to its other end it has a linear velocity of $I ω$

The average linear velocity of the rod, $v = \frac{l ω + 0}{2} = \frac{l ω}{2}$

Emf developed between the center and ring.

$\begin{array}{l} e = B l v = B l (\frac{l ω}{2}) = \frac{B l^{2} ω}{2} \\ = \frac{0.5 \times (1)^{2} \times 400}{2} = 100 V \end{array}$

Hence, the emf developed between the center and the ring is 100 V.

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