Question

A rectangular loop of metallic wire is of length a and breadth b and carries a current i. The magnetic field at the centre of the loop is-

• A. $\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi }$
• B. $\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi }$ $\frac { 4 \sqrt { a ^ { 2 } + b ^ { 2 } } } { a b }$
• C. $\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi }$
• D. $\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi }$ $\frac { \sqrt { a ^ { 2 } + b ^ { 2 } } } { a b }$

Answer 1

Answer: (A)

$\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi }$

Answer 2

B_AB = B_CD = $\frac { \mu _ { 0 } \mathrm { i } } { 4 \pi ( \mathrm {~b} / 2 ) }$ (sin f₁ + sin f₁) = $\frac { \mu _ { 0 } } { 4 \pi }$ . $\frac { 4 \mathrm { i } } { \mathrm { b } }$

$\frac { b } { \sqrt { a ^ { 2 } + b ^ { 2 } } }$

\ B = B_AB + B_BC + B_CD + B_DA

= $\frac { \mu _ { 0 } } { 4 \pi }$ .$\frac { \mu _ { 0 } } { 4 \pi }$ .