Question

A circular loop of radius $1m$ carries an electric current. Let $P$ and $Q$ be two points on the axis of the loop at distance $1m$ and $7m$ respectively from the center. If the magnetic field at P due to the current is $125mT$, then the magnetic field at $Q$ will be about :

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

Answer 1

The correct option is D $1mT$

$\left|B\right|$ =$\frac{2{\mu }_0.i.\pi r^2}{4\pi (r^2+x^2{)}^{3/2}}$

$\left|B\right|$ at P

$B_P=\frac{2{\mu }_0.i.\pi r^2}{4\pi (1+1{)}^{3/2}}=125mT$ ........... (1)

$\left|B\right|$ at Q

$B_Q=\frac{2{\mu }_0.i.\pi r^2}{4\pi (1+49{)}^{3/2}}$ ............(2)

On dividing (1) by (2), we will get,

$\frac{B_P}{B_Q}=(\frac{50}{2}{)}^{\frac{3}{2}}$

$\frac{125}{B_Q}=(\frac{50}{2}{)}^{\frac{3}{2}}$

On solving, we will get

$B_Q=1mT$