A short bar magnet has a magnetic moment of 0.48 J/T .Magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on the axis has a direction and magnitude of .a)1.06 G along S-N direction.b)0.96 G along S-N direction.c)0.86 G along S-N direction.d)0.76 G along S-N direction.Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Here M=0.48JT⁻¹,d=10cm=0.1m
On axis,
B= (μ₀/4π)(2M/d3)=10⁻⁷×(2×0.48/0.1³)=0.96×10⁻⁴T

Answer

Answer

Magnetic Moment of the Bar Magnet
The magnetic moment of a bar magnet is a measure of its strength and is defined as the product of the pole strength (magnetic strength) and the distance between the poles. It is denoted by the symbol m.

Given that the magnetic moment of the bar magnet is 0.48 J/T, we can write:

m = 0.48 J/T

Magnetic Field on the Axis of a Bar Magnet
The magnetic field produced by a bar magnet at a point on its axis can be calculated using the formula:

B = μ0 * (2m) / (4πr^3)

where B is the magnetic field, μ0 is the permeability of free space (4π x 10^-7 Tm/A), m is the magnetic moment of the bar magnet, and r is the distance from the center of the magnet to the point where the magnetic field is being calculated.

In this case, the distance from the center of the magnet is given as 10 cm, which is equivalent to 0.1 m. Plugging in the given values, we can calculate the magnetic field:

B = (4π x 10^-7 Tm/A) * (2 * 0.48 J/T) / (4π * (0.1 m)^3)
B = (2 * 0.48 J/T) / (0.1^3 m^3)
B = 0.96 J/(0.001 m^3 * T)
B = 0.96 T/A

Direction and Magnitude of the Magnetic Field
The magnitude of the magnetic field is given as 0.96 T/A. However, the question asks for the magnitude in Gauss (G), where 1 T = 10^4 G. Therefore, we need to convert the magnitude to Gauss:

0.96 T/A * 10^4 G/T = 9600 G

So, the magnitude of the magnetic field is 9600 G.

The direction of the magnetic field on the axis of a bar magnet is from the south pole to the north pole. Therefore, the correct answer is option 'B': 0.96 G along the S-N (south to north) direction.

Answer

Here M=0.48JT⁻¹,d=10cm=0.1m
On axis,
B= (μ₀/4π)(2M/d3)=10⁻⁷×(2×0.48/0.1³)=0.96×10⁻⁴T

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