Question

The effective length of a magnet is \(31.4 \mathrm{~cm}\) and its pole strength is \(0.5 \mathrm{~A} \mathrm{~m}\). The magnetic moment, if it is bent in the form of a semicircle will be Amp.m \(^{2}\) (a) \(0.1\) (b) \(0.01\) (c) \(0.2\) (d) \(1.2\)

Short answer

The magnetic moment of a magnet bent in the form of a semicircle with an effective length of \(31.4 \mathrm{~cm}\) and a pole strength of \(0.5 \mathrm{~A} \mathrm{~m}\) is \(0.1 \mathrm{~A} \mathrm{~m}^2\).

Step-by-step solution

Identify the given values

We are given the following information: - Effective length of the magnet = 31.4 cm - Pole strength of the magnet = 0.5 A m

Convert the effective length to meters

To carry out our calculations, we must convert the given effective length from cm to meters: Effective length of the magnet = 31.4 cm × (1 m / 100 cm) = 0.314 m

Calculate the diameter of the circle formed by the semicircle

Since the magnet is bent in the form of a semicircle, the effective length would represent half of the circumference of the formed circle. To find the diameter of the circle, we can use the formula for the circumference: Circumference = 2 × π × radius Let the radius of the circle be R. Then, the effective length equals half the circumference: 0.314 m = π × R Now, we can solve for R: R = 0.314 m / π ≈ 0.1 m The diameter of the circle, which represents the distance between the poles, is twice the radius: Diameter = 2 × R = 2 × 0.1 m = 0.2 m

Calculate the magnetic moment

Now that we know the distance between the poles (the diameter of the circle), we can calculate the magnetic moment using the formula: Magnetic moment = pole strength × distance between poles Magnetic moment = 0.5 A m × 0.2 m = 0.1 A m²

Select the correct option

The calculated magnetic moment is 0.1 A m². Hence, the correct option is: (a) 0.1