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A wire is bent in the form of a square o...

A wire is bent in the form of a square of side la in a varying magnetic field `B= prop B_(0)t hatk`. If the resistance per unit length is `lambda`. then find the following:
(i) The direction of induced current
(ii) The current in the loop
(iii) Potential difference between P and Q

Text Solution

Verified by Experts

(i) Direction of current is clockwise.
(ii) `|e|=(dphi)/(dt)=(d)/(dt)(BA)=a^(2)(d)/(dt)( alpha B_(0).t)=a^(2) alphaB`
Current : `i=(e)/(R)=(a^(2)alpha B_(0))/(4a lambda) ( :. R=4 a lambda) = (a alphaB_(0))/(4lambda)`
(iii) `V_(P)+(e)/(4)-i.alambda=V_(Q)`, where .e. is the total emf induced (or) `V_(P)-V_(Q)=i a lambda-(e)/(4)` (or) `V_(P)-V_(Q)= (e)/(4 a lambda). a lambda-(e)/(4)`
`V_(P)-V_(Q)=(e)/(4)-(e)/(4)=0`
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