Torque Problem (1 Viewer)

[MS8]

By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength?

(b) How many percent would the current need to be increased to return the torque to original values?

 

[jimmysmith560]

Would the following working help?

Part a):

Since the magnitude of the torque on a loop of area {A} that carries a current {I} whose area vector makes an angle {θ} with a magnetic field of density {B} is given by the equation:



So the ratio of the final torque on the loop after the decrease in B to the initial value is:

Therefore, the magnitude of the torque on the motor decreases by 5% too, as expected for any two linearly related variables.

Part b):

Since the final magnitude of the torque is equal to the initial one we can deduce the following relation:

Therefore:

Therefore, the current should increase by 5.26% to keep the magnitude of the torque constant.