Question

The magnetic field due to current carrying loop of radius $3cm$ at a point on the axis at a distance of $4$ cm from the centre is $54\mu$ T. Its value at the centre of the loop is :

• A. $250\mu$T
• B. $150\mu$T
• C. $125\mu$T
• D. $75\mu$T

Answer 1

Answer: (A)

$250\mu$T

Magnetic field the of loop $B=\frac{\mu i{R}^2}{2(X+R{)}^{3/2}}$

using the value for

$54=\frac{\mu \times i\times 3^2}{2(3+4{)}^{3/2}}$------------1

And at the center

$B=\frac{\mu i}{2\left(3\right)}$---------2

Dividing $1/2$

$\frac{54}{B}=\frac{3^3}{5^3}$

$B=\frac{54\times 5^3}{3^3}=250\mu T$