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:
Answer & explanation
Correct answer: option 4
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 -
$x=2cm$