A conducting bar of length L rotates with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown.A uniform magnetic field (magnitude = 0.20 T) is directed into the paper.If L = 0.40 m, what is the potential difference, VA - VP?

Question

Quizplus · Accepted Answer

We can use the formula for the induced EMF in a rotating conductor in a magnetic field:

EMF = B*L^2*w/2

where B is the magnetic field, L is the length of the conductor, and w is the angular velocity.

Substituting the given values, we get:

EMF = (0.20 T)*(0.40 m)^2*(2.0 rad/s)/2 = 0.016 V = 16 mV

However, we need to consider the direction of the induced EMF. By the right-hand rule, the direction of the induced current will be such that it opposes the change in magnetic flux. In this case, as the bar rotates, the area of the loop enclosed by the bar and the magnetic field decreases, so the induced current will create a magnetic field in the opposite direction to the external magnetic field. This means that the potential difference across the length of the bar will be from the end closest to the pivot point (which we will call point A) to the other end (which we will call point B).

Therefore, the potential difference VA - VB is given by:

VA - VB = EMF = 16 mV

But we need to find VA - VP, not VA - VB. Since the bar is rotating with a constant angular velocity, there is no potential difference between points B and P (since they are both at the same distance from the pivot point and are moving at the same speed). So we have:

VA - VP = VA - VB = 16 mV

Therefore, the answer is choice C: (F1F1F1S1F1F1F108.0 mV).

A Conducting Bar of Length L Rotates with a Constant