Question 46: Electromagnetic Induction

Question

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 $ \pi $ rad s
-1
about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? $(\pi=3.14)$

Accepted Answer

To determine the potential difference between the center and the rim of the disc (often called a Faraday disc or unipolar generator), we use the formula for motional EMF in a rotating disc:
$$ V = \frac{1}{2} B \omega R^2 $$
where:
$$B$$ is the magnetic field strength,
$$\omega$$ is the angular velocity,
$$R$$ is the radius of the disc.
Given:
$$B = 0.4\ 	ext{T}$$,
$$\omega = 10\pi\ 	ext{rad/s}$$,
$$R = 20\ 	ext{cm} = 0.2\ 	ext{m}$$,
we substitute these values into the formula:
First calculate $$R^2$$:
$$    R^2 = (0.2\ 	ext{m})^2 = 0.04\ 	ext{m}^2    $$
Substitute into the formula:
$$    V = \frac{1}{2} 	imes 0.4 	imes (10\pi) 	imes 0.04    $$
Multiply step-by-step:
$$0.4 	imes 10\pi = 4\pi$$,
Then, $$4\pi 	imes 0.04 = 0.16\pi$$,
Finally, multiply by $$\frac{1}{2}$$:
$$      V = \frac{1}{2} 	imes 0.16\pi = 0.08\pi      $$
Substitute $$\pi \approx 3.14$$:
$$    V \approx 0.08 	imes 3.14 = 0.2512\ 	ext{V}    $$
Thus, the potential difference developed between the axis and the rim is approximately $$0.2512\ 	ext{V}$$, which corresponds to Option C.

Answer

0.5024 V

Answer

0.0628 V

Answer

0.2512 V

Answer

0.1256 V

Electromagnetic Induction

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