Question

Points $A$ and $B$ are situated on an axis perpendicular to a $2cm$ long bar magnet at large distances $x$ and $3x$ from its center on opposite sides. The ratio of the magnetic field at $A$ and $B$ will be approximately equal to :

• A. $27:1$
• B. $2:9$
• C. $9:1$
• D. $1:9$

Answer 1

Answer: (A)

$27:1$

Magnetic field at A $B_A\propto \frac{1}{d_A^3}$
Magnetic field at B $B_B\propto \frac{1}{d_B^3}$
$\therefore \frac{B_A}{B_B}=\frac{d_B^3}{d_A^3}=\frac{(3x{)}^3}{x^3}=\frac{27}{1}$