Exercise 29.6 A coil 3.60 cm radius, containing 540 turns, is placed in a unifor

Question

Exercise 29.6 A coil 3.60 cm radius, containing 540 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×102 T/s )t+( 2.70×105 T/s4 )t4. The coil is connected to a 540- resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

Part A

Find the magnitude of the induced emf in the coil as a function of time.

Part B

What is the current in the resistor at time t0 = 4.75 s ?

A

E= 8.40×103 V +( 7.56×105 V/s3 )t3 E= 2.64×102 V +( 5.94×105 V/s3 )t3 E= 2.64×102 V +( 2.37×104 V/s3 )t3 E= 8.40×103 V +( 2.37×104 V/s3 )t3

Explanation / Answer

Ok, the problem is that the induced emf, is known by :

EMF= - N*d(flux) / dt

flux = B*area

And, you need to derivative the flux relative to time, so maybe that's the mistake, first you need to find the expression of the derivative and then replace the values from 0 to 4.75 seconds. So let's do it like that :

B = 1.2 * 10-2 t + 2.70*10-5 t4

area = pi*(3.60/100)2

flux = (1.2 * 10-2 t + 2.70*10-5 t4)*pi*(3.60/100)2  

then :

emf = -540*d((1.2 * 10-2 t + 2.70*10-5 t4)*pi*(3.60/100)2 ) / dt

emf = -2.19*d(1.2 * 10-2 t + 2.70*10-5 t4) / dt

Please calculate further.

Hope this helps. :) Also, not so sure of the calculations, however, you can rely on the logic.

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