Question

A wire in the form of a square of side a carries a current i. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = μ₀)

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

Answer 1

Answer: (C)

$\frac { 2 \sqrt { 2 } \mu _ { 0 } \mathrm { i } } { \pi \mathrm { a } }$

Answer 2

Magnetic field due to one side of the square at centre O

$B _ { 1 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 i \sin 45 ^ { \circ } } { a / 2 }$

⇒ $B _ { 1 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 \sqrt { 2 } i } { a }$

Hence magnetic field at centre due to all side