Two similar magnetic poles having pole strengths in the ratio 1 : 4 are placed 6 cm apart. The distance from a smaller pole in strength where net magnetic field is zero will be:

2 cm

The correct answer is Option (4) → 2 cm

The magnetic field due to a magnetic pole at distance 'r' from the pole -

$B=\frac{μ_0}{4\pi}.\frac{P}{r^2}$ [Biot Savart law]

where,

P - Pole strength

r - distance from pole

$B_1=\frac{μ_0}{4\pi}.\frac{P}{x^2}$

$B_2=\frac{μ_0}{4\pi}.\frac{4P}{(6-x)^2}$

and,

$B_1=B_2$

$⇒\frac{P}{x^2}=\frac{4P}{(6-x)^2}$

$\frac{1}{x^2}=\frac{4}{(6-x)^2}$

$36+x^2-12x=4x^2$

$3x^2+12x-36=0$

$x^2+4x-12=0$

$x^2+6x-2x-12=0$

$(x+6)(x-2)=0$

x = -6 or 2

Since, a negative distance doesn't make sense - 

$x=2cm$