A circular coil with n15000 turns is made of a conducting...

A circular coil with N1 = 5000 turns is made of a conducting material with resistance 0.0100 Î©/m and radius a = 40.0 cm. The coil is attached to a C = 10.00 Î¼F capacitor as shown in (Figure 1). A second coil with radius b = 4.00 cm, made of the same wire, with N2 = 100 turns, is concentric with the first coil and parallel to it. The capacitor has a charge of +100 Î¼C on its upper plate, and the switch S is open. At time t = 0, the switch is closed. What is the magnitude of the current in the smaller coil at t = 1.26 ms?

Transcript

00:01 Here we are given n1 is equal to 5000, r is equal to 0 .01 oom per meter, radius a is equal to 0 .4 meter, capacitance c is equal to 10 into 10 power minus 6 ferret, radius b is equal to 0 .04 meter, n2 is equal to 100 and charge q is equal to 100 into 10 power minus 6 coulum now first we need to write the resistance of bigger coil the resistance of bigger coil is given by r is equal to small r into 2 pi into radius a into n1 substituting the values here r is 0 .01 0 .00 ome per meter into 2 pi into radius a is 0 .4 meter into n1 is 5 ,000.

01:10 Upon solving we will get the resistance of bigger coil r is equal to 125 .6 om.

01:19 Next we need to calculate the voltage across capacitor.

01:27 The voltage across the capacitor is given by the v0 is equal to q0 by c which is equal to 100 into 10 power minus 6 divided by 10 into 10 power minus 6 this turns out to be 10 volt the maximum current in the bigger coil is given by i note is equal to v0 divided by r which is equal to 10 divided by 25 sorry 125 .6 this turn turns out to be 79 .6 into 10 power minus 3 amoeia.

02:11 Now the flux passing through smaller coil is to be calculated.

02:22 The flux passing through the smaller coil, 52 is equal to n2 into b1a2.

02:30 This is equal to n2 into magnetic field b1 is given by mu 0 into n1 into i divided by 2a into a2 is pi b square.

02:45 Here i is time dependent current, so i equal to i 0, e rise 2 minus t divided by r c and here r c is equal to 1 .26 millisecond which is time constant.

03:05 Now we have to substitute the values.

03:08 Here 5 -2 will be equal to mu 0 n1 n2 divided by 2 times the radius a into pi into b square into i -not e -raise 2 minus t divided by the time constant upon substituting first we need to write an equation for induced dmf induced dmf is equal to minus d 5 by d t that is we have to differentiate the above equation with respect to time t.

03:46 Or this is equal to upon differentiating we will get a mu zero n1 n2 pi b square into i0 divided by 2a r into c into e raise to minus t divided by rc.

04:07 Upon substituting the values, e is equal to mu zero is 4 pi...

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