Answer:


In this question, we are given two like magnetic poles of strength 25Am and 64Am respectively, and we need to find out at what point on the line joining the two poles, the magnetic field will be zero.


We know that like poles repel each other, and the magnetic field lines always go from the north pole to the south pole. Therefore, in this case, the magnetic field lines will go from the north pole of the 64Am pole to the south pole of the 25Am pole.


We can use the formula for the magnetic field due to a magnetic pole, which is given by:

B = (μ/4π) * (2m/r^2)

Where B is the magnetic field, μ is the magnetic permeability of air (4π * 10^-7 Tm/A), m is the strength of the magnetic pole, and r is the distance between the two poles.

We can calculate the magnetic field at a point P on the line joining the two poles, which is at a distance of x from the 64Am pole and (1-x) from the 25Am pole.

Therefore, the magnetic field at point P is given by:

B = (μ/4π) * [(2 * 64)/(x^2)] - [(2 * 25)/((1-x)^2)]


Now, we need to find the value of x for which the magnetic field at point P is zero.

Therefore, we can set the above equation equal to zero and solve for x:

(μ/4π) * [(2 * 64)/(x^2)] - [(2 * 25)/((1-x)^2)] = 0

Simplifying this equation, we get:

[(2 * 64)/(x^2)] = [(2 * 25)/((1-x)^2)]

Solving for x, we get:

x = 0.538

Therefore, the point on the line joining the two poles, where the magnetic field is zero, is at a distance of 0.538 m from the 64Am pole and 0.462 m from the 25Am pole.


In conclusion, we have calculated the point on the line joining two like magnetic poles of strength 25Am and 64Am respectively, where the magnetic field is zero. We have used the formula for the magnetic field due to a magnetic pole and solved for the distance between the two poles where the magnetic field is zero.