Question

The earth’s magnetic induction at a certain point is $7 \times 10 ^ { - 5 } \mathrm {~Wb} / \mathrm { m } ^ { 2 }$ . This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius 5 cm. The required current in the loop is

• A. .56 A
• B. 5.6 A
• C. 0.28 A
• D. 2.8 A

Answer 1

Answer: (B)

5.6 A

Answer 2

Circular coil Square coil

Length L = 2π r Length L = 4a

Magnetic field $B = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 \pi i } { r }$ $= \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 4 \pi ^ { 2 } i } { r }$

$B = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 \sqrt { 2 } i } { a }$ $B = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 8 \sqrt { 2 } i } { a }$

Hence $\frac { B _ { \text {circular } } } { B _ { \text {square } } } = \frac { \pi ^ { 2 } } { 8 \sqrt { 2 } }$