A circular loop of wire with radius 0.0250 m and resistance 0.400 is in a region

Question

A circular loop of wire with radius 0.0250 m and resistance 0.400 is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins increasing, with B(t)=( 0.340 T/s3 ) t3 .

Part A

What is the current in the loop

(magnitude) at the instant when 1.44 T ?

Express your answer with the appropriate units.

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A circular loop of wire with radius 0.0250 m and resistance 0.400 is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins increasing, with B(t)=( 0.340 T/s3 ) t3 .

Part A

What is the current in the loop

(magnitude) at the instant when 1.44 T ?

Express your answer with the appropriate units.

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Explanation / Answer

the induced emf is

= - dB / dt

where, B = A B = r2 [ ( 0.340 T/s3 ) t3 ]

then

= - dB / dt = -d{ r2 [ ( 0.340 T/s3 ) t3 ] } / dt = - ( 0.680 T/s3 ) r2 t2  

Hence, the current is

i = / [ ( 0.680 T/s3 ) r2 t2 ]

when t=1.44

i = [ ( 0.680 T/s3 ) r2 t2 ] / R

i = [ ( 0.680 T/s3 ) ( 0.0250 m )2 ( 1.44 s)2 ] / ( 0.400 is  )

i = 0.0069 A

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