Question 323: Electromagnetic Induction

Question

A wire of length '$$L$$'; having resistance '$$R$$' falls from a height '$$\ell$$' in earth's horizontal magnetic field '$$B$$'. The current through the wire is ( $$\mathrm{g}=$$ acceleration due to gravity)

Accepted Answer

If the wire falls through a height $$h$$, the velocity acquired by it is $$\mathrm{v}=\sqrt{2 \mathrm{~g} \ell}$$
The emf induced in the wire
$$\begin{aligned}
& \mathrm{e}=\mathrm{BLv}=\mathrm{BL} \sqrt{2 \mathrm{~g} \ell} \
	herefore 	ext { Current } \mathrm{I} & =\frac{\mathrm{e}}{\mathrm{R}}=\frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}}
\end{aligned}$$

Answer

$$\frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}}$$

Answer

$$\frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}^2}$$

Answer

$$\frac{2 \mathrm{BLg} \ell}{\mathrm{R}^2}$$

Answer

$$\frac{\mathrm{B}^2 \mathrm{~L}^2}{\mathrm{R}}$$

Electromagnetic Induction

A wire of length '$L'; having resistance 'R' falls from a height '\ell' in earth's horizontal magnetic field 'B'. The current through the wire is ( \mathrm{g}=$ acceleration due to gravity)

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