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As shown in figure, a long wire kept vertically on the plane of paper carries electric current-I. A conducting ring moves towards the wire with velocity v with its plane conducting with the plane of paper. Find the induced emf produced in the ring when it is at a perpendicular distance r from the wire. Radius of the ring is a and a lt lt r. |
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Answer» Solution :Magnetic FIELD at a distance r from the wire carrying current is `B =(mu_0I)/(2pir)` `THEREFORE` Magnetic flux linked with the RING, `phi=B(pia^2)` `=(mu_0I)/(2pir)xxpia^2` `=(mu_0Ia^2)/(2r)` `therefore` EMF `epsilon=-(dphi)/(dt)` `=-d/(dt)((mu_0Ia^2)/(2r))` `=(mu_0Ia^2)/2 (1/r^2)(dr)/(dt)` `therefore epsilon = (mu_0Ia^2)/(2r^2) v (because (dr)/(dt)=v)` |
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