F if the loop radius is r 30 cm and the magnetic field is...

f) If the loop radius is r = 30 cm and the magnetic field is that of the earth's B = 40 μT, how fast must the loop rotate (in rotations per second) in order to induce an EMF of ε = 1 V?

Transcript

00:01 Hi, here in this given problem first of all we draw the variation in magnetic field with the passage of time.

00:10 Magnetic field is taken over the y -axis as a multiple of 10 to the bar minus 3, tesla.

00:19 And time in millisecond over the x -axis.

00:24 First of all, magnetic field increases linearly up to a value of 3 multiplied by 10 to minus 3 tesla, up to a time 2 .0 milliseconds.

00:45 Then the current remains constant up to 5 milliseconds and then drops to 0 in the next 1 second.

00:54 So here it is this is 2 .0 milliseconds.

00:59 This is 5 .0 millisecond.

01:01 This is 6 .0 milliseconds.

01:03 And here the maximum magnetic field that is 3 .0 mili tesla it will be.

01:09 Ok.

01:10 Now radius of circular loop, radius of the circular loop, that is given as r is equal to 11 centimeter.

01:27 Or we can say this is 0 .11 meter.

01:31 Now in the first part of the problem, we have to find a f induced at a time t1 is equal to 1 .0 millisecond means from 0 to 2 milliseconds somewhere here so that will be given by using faraday's laws of electromagnetic induction e1 is equal to d5 by d t 5 means the magnetic flux is given as product of magnetic field with the area of the circular loop as the magnetic field is perpendicular to the area.

02:09 So this the flux will be given by b into a.

02:12 Now area will remain constant and this is a multiplied by db by d t...

Question

f) If the loop radius is r = 30 cm and the magnetic field is that of the earth's B = 40 μT, how fast must the loop rotate (in rotations per second) in order to induce an EMF of ε = 1 V?

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