Question

A conducting wire formed in the shape of a right triangle with base b = 38 cm and height h = 65 cm and having resistance R = 1.1 Ω, rotates uniformly around the y-axis in the direction indicated by the arrow (clockwise as viewed from above (loooking down in the negative y-direction)). The triangle makes one complete rotaion in time t = T = 1.8 seconds. A constant magnetic field B = 1.1 T pointing in the positive z-direction (out of the screen) exists in the region where the wire is rotating.

1)

What is ω, the angular frequency of rotation?

radians/second

2)

What is I_max, the magnitude of the maximum induced current in the loop?

A

3)

At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux Φ₁ at time t = t₁ = 0.675 s?

T-m²

4)

What is I₁, the induced current in the loop at time t = 0.675 s? I₁ is defined to be positive if it flows in the negative y-direction in the segment of length h.

A

5)

Which of the folowing statements about Φ_o, the magnitude of the flux through the loop at time t = t_o = 0.45 s, and I_o, the magnitude of the current through the loop at time t = t_o = 0.45 s, is true? Φ_max and I_max are defined to be the maximum values these quantites achieve during the complete rotation.

Φ_o = 0 and I_o = 0

Φ_o = 0 and I_o = I_max

Φ_o = Φ_max and I_o = 0

Φ_o = Φ_max and I_o = I_max

6)

Suppose the frequency of rotation is now doubled. How do Φ_max, the maximum value of the flux through the loop, and I_max, the maximum value of the induced current in the loop change?

Φ_max and I_max both double

Φ_max doubles and I_max remains the same

Φ_max remains the same and I_max doubles

Both Φ_max and I_max remain the same