A wire bent as a parabola y = k x 2 is located in a uniform magnetic field of induction B , the vector B being perpendicular to the plane x y . At t = 0 , the sliding wire starts sliding from the vertex O with a constant acceleration a linearly as shown in Fig. Find the emf induced in the loop -

Question

A wire bent as a parabola y = k x 2 is located in a uniform magnetic field of induction B , the vector B being perpendicular to the plane x y . At t = 0 , the sliding wire starts sliding from the vertex O with a constant acceleration a linearly as shown in Fig. Find the emf induced in the loop -, B y 2 a k, B y 4 a k, B y 8 a k, B y a k

MARKS App · Accepted Answer

d ϕ = B . d A = 2 B x d y and y = k x 2 ∴ x = y k ∴ Emf E = d ϕ d t = 2 B y k d y d t using v 2 = 2 a s d y d t = v = 2 a y or ε = d ϕ d t = 2 B y k 2 a y or ε = B y 8 a k

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