Question

An infinitely long straight conductor is bent into the shape as shown in fig. the magnetic induction at the centre of circular loop is

Answer 1

An infinitely long straight conductor is bent into the shape as shown in fig. the magnetic induction at the centre of circular loop is

μ₀i/2πR(π+1)

Answer 2

Answer: $=\frac { \mu _{ 0 }i }{ 2R } \left[ 1\quad +\quad \frac { 1}{ \pi}\right]$

There are two currents that contribute to the magnetic field at the centre of the loop.  

They are

i) The magnetic field due to the circular loop

ii) The magnetic field due to the conducting wire.

The equation for the first one

                  $B_{ 1 }=\frac { \mu _{ 0 }i }{ 2R } \quad \longrightarrow \left( 1 \right)$

The equation for the second one

                  $B_{ 2 }=\frac { \mu _{ 0 }i }{ 2\pi R } \quad \longrightarrow (2)$

Hence the total magnetic field is

                  $=\frac { \mu _{ 0 }i }{ 2R } +\frac { \mu _{ 0 }i }{ 2\pi R }$

On taking common, $=\frac { \mu _{ 0 }i }{ 2R } \left[ 1\quad +\quad \frac { 1 }{ \pi }\right]$