Question

Two like magnetic poles of strength 10 and 40 SI units are separated by a distance 30 cm. The
intensity of magnetic field is zero on the line joining them
(A) At a point 10 cm from the stronger pole
(B) At a point 20 cm from the stronger pole
(C) At the mid-point
(D) At infinity

Answer 1

Given that,

Magnetic poles strength = 10

Magnetic poles strength = 40

Distance = 30 cm

Let the intensity of magnetic field is zero at x cm.

We need to calculate the intensity of magnetic field

Using formula of intensity

$I=\dfrac{\mu_{0}}{4\pi}\dfrac{M}{d^2}$

Put the value into the formula

For 10 magnetic pole,

$I=\dfrac{\mu_{0}}{4\pi}\dfrac{10}{x^2}$....(I)

For 40 magnetic pole,

$I=\dfrac{\mu_{0}}{4\pi}\dfrac{40}{(30-x)^2}$....(II)

From equation (I) and (II)

$\dfrac{\mu_{0}}{4\pi}\dfrac{10}{x^2}=\dfrac{\mu_{0}}{4\pi}\dfrac{40}{(30-x)^2}$

$(30-x)^2=4x^2$

$3x=30$

$x=10\ cm$

Hence, The  intensity of magnetic field is zero at a point 10 cm from the stronger pole.

(A) is correct option.