A magnetic field passes through a stationary wire loop, and its magnitude change

Question

A magnetic field passes through a stationary wire loop, and its magnitude changes in time according to the graph in the drawing. The direction of the field remains constant., There are three equal time intervals indicated in the graph: 0 4.0 s, 4.0 8.0 s, and 8.0 2.0 s. The loop consists of 52 turns of wire and has an area of 0.11 m^2. The magnetic field is oriented parallel to the normal to the loop. What is the Induced EMF (epsilon) for each (show at least one setup) 0 - 4 sec 4 - 8 sec 8 - 12 sec A Magneto Hydrodynamic generator has a conducting fluid flowing a 200 m/sec through a perpendicular magnetic field of 0.37 T. The tube has a radius of 4 cm, and has contacts connected to either side of the tube. How much EMF (epsilon) would this arrangement produce in Induced Votage? (epsilon) ___ Volts

Explanation / Answer

(a) The emf is given by the rate of change of flux.

emf = -N*A*(delta B/delta t)

N = 52 turns, A = 0.11 m^2

For the first section of the graph, (delta B/delta t) = (0.3 T- 0.12 T)/(4 s - 0 s)

= -9/20 T/s

emf = -52*0.11*(-9/20)

= 2.57 volts (counterclockwise )

For the second section of the graph, (delta B/delta t) = (0.3 T- 0.3 T)/(8 s - 4 s)

= 0 T/s

emf = -52*0.11*0

= 0 volt

For the third section of the graph, (delta B/delta t) = (0.9 T- 0.3 T)/(12 s - 8 s)

= 3/20 T/s

emf = -52*0.11*(3/20)

= -0.858 volt (clockwise )

(c) Given; mass m = 3 mg = 3*10^-6 kg

charge q = 15*10^-9 C

the radius of its orbit is

r = q/m

= 15*10^-9/3*10^-6

= 5*10^-3 m

r = 5 mm

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