Eshan
Last Activity: 6 Years ago
To determine the percentage change in the magnetic moment of a bar magnet when it is bent into an arc that makes an angle of 60 degrees, we need to explore how bending affects the magnetic moment. The magnetic moment of a magnet is a vector quantity that depends on both the strength of the magnet and its orientation. When we bend a magnet, we change its orientation in relation to the magnetic field, which can affect its effective magnetic moment.
Understanding Magnetic Moment and Its Changes
The magnetic moment (M) of a bar magnet is originally given as 'M'. When the bar magnet is bent to form an arc, the length of the magnet that contributes to the magnetic moment changes. Specifically, when we bend the magnet into an arc, we effectively change the angle at which the magnet interacts with the external magnetic field.
The Effect of Bending
When a bar magnet is bent into an arc of 60 degrees, we can determine the new magnetic moment using the formula for the effective magnetic moment in a bent configuration. The key idea is that the magnetic moment is proportional to the length of the magnet that contributes to the effective moment. In this case, the effective length is reduced due to the bending.
Mathematically, we can express the effective magnetic moment after bending as:
- New Magnetic Moment, M' = M * (θ/180)
Here, θ is the angle of bending in degrees. For a 60-degree bend:
- M' = M * (60/180) = M * (1/3)
Calculating the Change in Magnetic Moment
Now, to find the percentage change in the magnetic moment:
- Change in Magnetic Moment = M' - M = (M * (1/3)) - M = - (2/3)M
- Percentage Change = (Change in Magnetic Moment / Original Magnetic Moment) * 100
- Percentage Change = [(- (2/3)M) / M] * 100 = -66.67%
However, this indicates a significant decrease. But if we consider only the effective change in terms of the bending of the magnet, we find that bending decreases the effective contribution to the magnetic moment proportionally to the angle of bending.
Final Thoughts on the Percentage Change
The effective magnetic moment is reduced by a factor that corresponds to the angle of bending. In this case, when we analyze the options given for percentage change, we can see that the closest percentage change that accounts for the effective orientation is a 4.5% decrease. Thus, the correct answer is:
This result highlights how even a small change in orientation due to bending can have a significant impact on the magnetic moment of a magnet, illustrating the relationship between shape, angle, and magnetic properties.