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A square loop of side 'a' with a capacit...

A square loop of side 'a' with a capacitor of capacitance C is located between two current carrying long parallel wires as shown. The value of I in the wires in given as `I=(I_0) sin omega t`.

(a) Calculate maximum current in the square loop.
(b) Draw a graph between charges on the upper plates of the capacitor vs time.

Text Solution

Verified by Experts

`(a)` Flux through the square loop
`=int_(a)^(2a)(mu_(0))/(4pi)2I|(1)/(x)+(1)/(3a-x)|adx=(mu_(0))/(4pi)Ia4ln2`
Induced emf `e=-(dphi)/(dt)=-(mu_(0))/(pi)aI_(0)omegaln2cosomegat`
Charge on the capacitor
`Q=Ce=-C(mu_(0))/(pi)aI_(0)omegaln2cosomegat=-Q_(0)cosomegat` (say)
Current in the loop `=(dQ)/(dt)=(mu_(0))/(pi)CI_(0)omega^(2)aln2sinomegat`
`I_(max)=(mu_(0))/(pi)CI_(0)aomega^(2)ln2`

`(b)`
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