Question

The magnetic induction at the centre O in the figure shown is

• A. $\frac { \mu _ { 0 } i } { 4 } \left( \frac { 1 } { R _ { 1 } } - \frac { 1 } { R _ { 2 } } \right)$
• B. $\frac { \mu _ { 0 } i } { 4 } \left( \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } } \right)$
• C. $\frac { \mu _ { 0 } i } { 4 } \left( R _ { 1 } - R _ { 2 } \right)$
• D. $\frac { \mu _ { 0 } i } { 4 } \left( R _ { 1 } + R _ { 2 } \right)$

Answer 1

Answer: (A)

$\frac { \mu _ { 0 } i } { 4 } \left( \frac { 1 } { R _ { 1 } } - \frac { 1 } { R _ { 2 } } \right)$

Answer 2

In the following figure, magnetic fields at O due to sections 1, 2, 3 and 4 are considered as $B _ { 1 } , B _ { 2 } , B _ { 3 }$ and $B _ { 4 }$ respectively.

$B _ { 1 } = B _ { 3 } = 0$

$B _ { 2 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { \pi i } { R _ { 1 } } \otimes$

$B _ { 4 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { \pi i } { R _ { 2 } }$◉ As $\left| B _ { 2 } \right| > \left| B _ { 4 } \right|$

So