ele401week11

# ele401week11 - t ﬂowing in the loop(c Is V 1 = V 2 B y x...

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ELE401 - Field Theory: Tutorial Problems Week 11 1. The loop shows in Figure 1 is rotating about the z-axis in the ˆ a φ direction at w [rad/s]. There is a magnetic ﬂux density ﬁeld -→ B = ( B 1 t + B 0 ) ˆ a x [T] present. (a) Solve for the voltage across the resistor R using V emf = H ( ~u × -→ B ) · d ~ l . (b) Indicate the direction of the current ﬂowing in the loop and solve for the voltage across the resistor R using V emf = - ∂ψ ∂t and why is this answer diﬀerent from 1a? (c) Solve for the instantaneous power p ( t ), where p ( t ) = V 2 emf R . B A C D R B B B x y z Figure 1: Revolving wire loop 1

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2. If -→ B = 0 . 2 cos 150 πt ˆ a z , (a) Solve for the voltage induced in the loop from Figure 2 (the loop is not moving). (b) Solve for the current i
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Unformatted text preview: ( t ) ﬂowing in the loop. (c) Is V 1 = V 2 ? B y x 1 1 2 2 R = 10 W 1 R = 5 W 2 V 1 + _ V 2 + _ Figure 2: Wire loop 3. The loop in Figure 3 is in motion with velocity ~u =-u o ˆ a y [m/s]. The ﬂux density is-→ B = B o e-αy ˆ a z [T]. (a) Solve for V AB , V DC , and V emf . Hint: V emf = V AB-V DC (b) Solve for the current. x z y R /2 R /2 A B C D-a/2 a/2 y y+b B u Figure 3: Wire loop 2 4. If-→ B in Figure 4 is-→ B = B o ˆ a z , solve for the voltage on the meter and indicate polarity. V z w r = a Conducting Shaft Contact Voltmeter Copper Disk B Figure 4: Faraday Homopole Generator 3...
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ele401week11 - t ﬂowing in the loop(c Is V 1 = V 2 B y x...

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