A current i is flowing in a straight conductor of length L. The magnetic field at a point distant L 4 from its centre will be Options: A . &nbsp4μ0i√5πL B . &nbsp4μ0i2πL C . &nbspμ0i√2L D . &nbspZero

Answer: Option A : A By using B = μ 0 4 π . i a ( s i n ϕ 1 + s i n ϕ 2 ) ⇒ B = μ 0 4 π . i ( L / 4 ) ( 2 s i n ϕ ) Also s i n ϕ = L / 2 √ 5 L / 4 = 2 √ 5 ⇒ B = 4 μ 0 i √ 5 π L

A current i is flowing in a straight conductor of length L. The magnetic field a

Question

A current i is flowing in a straight conductor of length L. The magnetic field at a point distant

\frac{L}{4}

from its centre will be

Options:

A . 4μ0i√5πL

B . 4μ0i2πL

C . μ0i√2L

D . Zero

Answer: Option A
:
A

A Current I Is Flowing In A Straight Conductor Of Length L. ...

By using

B = \frac{μ_{0}}{4 π} . \frac{i}{a} (s i n ϕ_{1} + s i n ϕ_{2})

\Rightarrow B = \frac{μ_{0}}{4 π} . \frac{i}{(L / 4)} (2 s i n ϕ)

Also

s i n ϕ = \frac{L / 2}{\sqrt{5} L / 4} = \frac{2}{\sqrt{5}}

\Rightarrow B = \frac{4 μ_{0} i}{\sqrt{5} π L}

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