PROBLEM 6. A piece of wire that of the lower circle is 9.00 is shaped into a fig

Question

PROBLEM 6. A piece of wire that of the lower circle is 9.00 is shaped into a figure 8. The radius of the upper circle is 5.00 cm and ' Rob . i'', rele is 9.00 cm. A 7 00- resistor is connected asse direction Shown. /s of 2.00 T is applied perpendicular to the plane of the two circles, in the direction s (a) Find the magnitude of the current flowing through the resistor if the magnetic field doubles in 4.00 s 5.00 cm XXXx 100 T.osmSixlo A not corrc applica ion 9.00 cm d. 7.00 (b) Does the current in the resistor flow from left-to-right or from right-to-left in the picture? Explain your reasoning. Jwc Page 4

Explanation / Answer

(a) From Lenz law, the change in magnetic field through loop Will be opposed by the loop. This will be done by an induced emf, whose current Will be such that this current's magnetic field Will try to reduce the effect of changing magnetic field. So for increasing downwards magnetic field, induced current Will be such as to generate upwards magnetic field through the loops.

External field is into the paper, so from Lenz law, rise in external field Will generate an emf, so as to flow anti clockwise current in upper coil and lower coil. But they are connected in such way that these emfs are in opposite direction.

So, emf(total)=emf1(larger loop)- emf2(smaller loop) {direction of emf same as that of emf1}

Using the relation for emf, emf2= change in magnetic flux/time = change in magnetic field*area/4= (4-2)*pi*0.05^2 /4= 3.9*10^-3 V

Similarly, emf1= change in magnetic flux/time = (4-2)*pi*0.09^2 /4= 0.0127 V

so, emf= 0.0127-0.0039= 0.0088V

so, using i=emf/resistance;

or, i=0.0088/7= 0.00125A

(b) This current is due to emf, as discussed above, it's direction is such as to flow anti clockwise current in larger loop. So with anti clockwise current in larger loop, the current direction in resistor is from left to right.

please upvote if understood to appreciate

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