A bar magnet of 5 cm long having a pole strength of 20 A.m. is deflected through 30 degrees , from the magnetic meridian . If H is = 320/4*pi A/m , then what is the deflecting couple ?

To find the deflecting couple acting on the bar magnet, we can use the formula that relates the magnetic moment, the magnetic field strength, and the angle of deflection. The couple on a magnetic dipole in a magnetic field can be expressed as the product of the magnetic moment and the magnetic field strength, multiplied by the sine of the angle between them. Let's break this down step by step.

Understanding the Components

First, we need to calculate the magnetic moment (M) of the bar magnet. The magnetic moment is defined as the product of the pole strength (p) and the length of the magnet (l). In this case:

• Pole strength (p): 20 A.m
• Length (l): 5 cm = 0.05 m

The formula for the magnetic moment is:

M = p × l

Substituting the values, we get:

M = 20 A.m × 0.05 m = 1 A.m²

Magnetic Field Strength

Next, we have the magnetic field strength (H), given as:

H = 320 / (4π) A/m

To simplify this, we can calculate H:

H ≈ 25.46 A/m (using π ≈ 3.14)

Calculating the Deflecting Couple

Now that we have the magnetic moment and the magnetic field strength, we can find the deflecting couple (τ) using the formula:

τ = M × H × sin(θ)

Here, θ is the angle of deflection, which is 30 degrees. We need to convert this angle into radians for our calculations:

sin(30°) = 0.5

Now we can substitute all the known values into the couple formula:

τ = 1 A.m² × 25.46 A/m × 0.5

Calculating this gives:

τ = 12.73 N.m

Final Result

Therefore, the deflecting couple acting on the bar magnet is approximately 12.73 N.m.

This calculation illustrates how the interaction between a magnetic dipole and an external magnetic field results in a mechanical torque or couple, which can be crucial in various applications, such as in designing magnetic compasses and other instruments that rely on magnetic properties.