Question

The magnetic field due to a short magnet, at a point on its axis, at a distance $X\text{cm}$ from the middle point of the magnet, is $200\text{Gauss}$. The magnetic field at a point on the equatorial axis, at a distance $X\text{cm}$ from the centre of magnet, will be

• A. $100\text{Gauss}$
• B. $400\text{Gauss}$
• C. $50\text{Gauss}$
• D. $200\text{Gauss}$

Answer 1

The correct option is A $100\text{Gauss}$

For axial point at a distance $X\text{cm}$ from the centre,

$\left|\overrightarrow{B}\right|=\frac{2KM}{X^3}=200\text{Gauss}$

For an equitorial point at same distance, $X\text{cm}$ from the centre,

$\left|\overrightarrow{B^{\prime }}\right|=\frac{KM}{X^3}=\frac{1}{2}\left(\frac{2KM}{X^3}\right)$

$\left|\overrightarrow{B^{\prime }}\right|=\frac{1}{2}\left(200\right)=100\text{Gauss}$

Hence, option $\left(A\right)$ is the correct answer.