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

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of amgnetic flux

induced current i = e/R

where R = resisatnce

t^3 = 0.144/0.34

t = 0.75 secs

so emf e = 1 * 3.14 * 0.025^2 * 0.144/0.75

emf e = 0.37 mV

induced current i = emf/R

i = 0.37 e -3/(.4)

i = 0.92 mA

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