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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 .a. in a varying magnetic field `vecB ='alpha'B_0 t hat k` . If the resistance per unit length is `lamda` , 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 alpha B`
Current i` = e/R = (a^2 alpha B_0)/(4 a lamda) (because R = 4a lamda)= (a alpha B_0)/(4 lamda)`
(iii) `V_P + e/4 - i alpha lamda = V_Q`
Where .e. is the total emf induced
` V_P -V_Q = i a lamda - e/4 " or " V_P - V_Q = (e )/(4a lamda). a lamda - e/4`
` V_P -V_Q = e/4 - e/4 = 0`
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