Question

Radius of current carrying coil is R. Then ratio of magnetic fields at the centre of the coil to the axil point, which is $R\sqrt{3}$ distance away from the centre of the coil

• A. $1:1$
• B. $1:2$
• C. $1:4$
• D. $8:1$

Answer 1

The correct option is D $8:1$

Given: Radius of the coil=R

Solution: The value of magnetic field at any point on the axial line is given by,

$B=\frac{{\mu }_{0}i{R}^2}{(R^2+x^2{)}^{\frac{3}{2}}}$ (1)

Magnetic field at the middle of the coil (x=0)

$B=\frac{{\mu }_{0}i}{2R}$ (From (1)) (2)

Magnetic field at $x=R\sqrt{3}$

$B=\frac{{\mu }_{0}i}{16R}$ (3)

On dividing equation (2) by (3) we get ratio equals to 8:1.

Hence the correct option is (D).