Question

Radius of a current carrying coil is 'R' . The ratio of magnetic field at a axial point which is R distance away from at the center of the coil and field at center of coil is

• A. ${\left(\frac{1}{2}\right)}^{1/2}$
• B. $\frac{1}{2}$
• C. ${\left(\frac{1}{2}\right)}^{3/2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C ${\left(\frac{1}{2}\right)}^{3/2}$

Given: Radius=R, current=I

Solution: As we know the formula of magnetic at a distance x in in the axis of current carrying coil:

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

At distance x=R ,$B=\frac{{\mu }_{0}I{R}^2}{2(2R^2{)}^{\frac{3}{2}}}.......\left(1\right)$

At the centre ,B$=\frac{{\mu }_{0}I}{2R}.......\left(2\right)$

Ratio of 1 and 2=$(\frac{1}{2}{)}^{\frac{3}{2}}$

Hence the correct option is C