A coil 3.65 cm radius, containing 540 turns, is placed in a uniform magnetic fie

Question

A coil 3.65 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+(2.80×105 T/s4 )t4. The coil is connected to a 660- resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

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

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

Possible Choices

E= 8.63×103 V  +( 2.53×104 V/s3 )t3

What is the current in the resistor at time t0 = 4.90 s ?

E= 8.63×103 V +( 8.06×105 V/s3 )t3 E= 2.71×102 V +( 6.33×105 V/s3 )t3 E= 2.71×102 V +( 2.53×104 V/s3 )t3

E= 8.63×103 V  +( 2.53×104 V/s3 )t3

Explanation / Answer

given

r = 3.65 cm = 0.0365 m

N = 540 turns

B = 0.012*t + 2.8*10^-5 t^4

R = 660 ohms

area of the loop, A = pi*r^2

= pi*0.0365^2

= 4.185*10^-3 m^2

induced emf = N*A*dB/dt

= 540*(4.185*10^-3)*(0.012 + 2.8*10^-5*4*t^3)

= 2.26*(0.012 + 2.8*10^-5*4*t^3)

= 2.71*10^-2 + 2.53*10^-4 t^3

so, Option 3) E= 2.71×102 V +( 2.53×104 V/s3 )t3 is the correct answer.

at t = 4.9 s

induced emf = 2.71*10^-2 + 2.53*10^-4*(4.9)^3

= 0.0568 Volts

induced current = induced emf/R

= 0.0568/660

= 9.5*10^-5 A

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