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Question: A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle \(3 \pi...

A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3π/23 \pi / 2 radian at its centre. The magnetic induction B at the centre is

A

μ0iR\frac { \mu _ { 0 } i } { R }

B

μ0i2R\frac { \mu _ { 0 } i } { 2 R }

C

2μ0iR\frac { 2 \mu _ { 0 } i } { R }

D

3μ0i8R\frac { 3 \mu _ { 0 } i } { 8 R }

Answer

3μ0i8R\frac { 3 \mu _ { 0 } i } { 8 R }

Explanation

Solution

B=μ04π(2π−θ)iR=μ04π(2π−π2)×iRB = \frac { \mu _ { 0 } } { 4 \pi } \frac { ( 2 \pi - \theta ) i } { R } = \frac { \mu _ { 0 } } { 4 \pi } \frac { \left( 2 \pi - \frac { \pi } { 2 } \right) \times i } { R } =3μ0i8R= \frac { 3 \mu _ { 0 } i } { 8 R }