Calculate the maximum value of the emf induced between the ends of the conductor.

+4 votes

In the figure below, a semicircular conductor of radius R = 0.300 m is rotated about the axis AC at a constant rate of 200rev/min. A uniform magnetic field of magnitude 1.22 T fills the entire region below the axis and is directed out of the page.

image
(a) Calculate the maximum value of the emf induced between the ends of the conductor.
 V

(b) What is the value of the average induced emf for each complete rotation?
 V

(c) How would your answers to parts (a) and (b) change if the magnetic field were allowed to extend a distance Rabove the axis of rotation? (Select all that apply.)

 

asked Feb 28, 2012 in Physics by awesome ~Expert~ (1,479 points)
    

1 Answer

+5 votes
 
Best answer

The formula for emf is:

max emf = B*A* ω    (*where B = magnetic field, A = area, ω = angular acceleration)

ω  = 200 rev/min = 200 rev / /60 s = 2π*200/60  rad/s  

ω = 2π*(10/3)  rad/s

 

B = 1.22 T

r = 0.3 m

A = (π*r^2) / 2  =  (π*(0.3 m)^2) / 2  (*notice its only half circle)

plugging back into the formula for emf we get:

max emf = (1.22 T)*(π*(0.3 m)^2) / 2 )*(2π*(10/3)  rad/s)

max emf = 3.61 V

 

Part B:

average emf is calculated as follows:

 

Part C, they would both remain unchanged

answered Mar 7, 2012 by Roar3215 ~Expert~ (1,318 points)
selected Mar 7, 2012 by awesome



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