A current i is flowing in a straight conductor of length L. The magnetic induction at a point distant frac{L}{4} from its centre will be

Q: A current $i$ is flowing in a straight conductor of length $L$. The magnetic induction at a point distant $\frac{L}{4}$ from its centre will be

a (a) By using $B = \frac{{{\mu _0}}}{{4\pi }}.\frac{i}{a}(\sin {\varphi _1} + \sin {\varphi _2})$ $ \Rightarrow B = \frac{{{\mu _0}}}{{4\pi }}.\frac{i}{{(L/4)}}(2\sin \varphi )$ Also $\sin \varphi = \frac{{L/2}}{{\sqrt 5 L/4}} = \frac{2}{{\sqrt 5 }}$$ \Rightarrow B = \frac{{4{\mu _0}i}}{{\sqrt 5 \pi L}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A current $i$ is flowing in a straight conductor of length $L$. The magnetic induction at a point distant $\frac{L}{4}$ from its centre will be

A$\frac{{4{\mu _0}i}}{{\sqrt 5 \pi L}}$
B$\frac{{{\mu _0}i}}{{2\pi L}}$
C$\frac{{{\mu _0}i}}{{\sqrt 2 L}}$
D
Zero

Diffcult

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

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