JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Magnetic Effects of Current

The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is

X 2 \times 1 0^{- 7} T

. The value of X is

Answer: 40

Solution

For a square loop of side

a = 1 m

carrying current

i = 5 A

, each side is a finite straight wire at perpendicular distance

d = a /2 = 0.5 m

from the center. The field due to one side, using the finite-wire formula with each end subtending

4 5^{\circ}

, is

B_{s i d e} = \frac{μ _{0} i}{4 π d} (sin 4 5^{\circ} + sin 4 5^{\circ}) = \frac{μ _{0} i}{4 π d} \cdot 2

All four sides contribute fields in the same direction at the center, so the total field is

B = 4 \times \frac{μ _{0} i}{4 π ( 0.5 )} \times 2 = \frac{4 \times 1 0 ^{- 7} \times 5 \times 2 \times 2}{1} = 402 \times 1 0^{- 7} T

X = 40

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Integer answer