A loop rectangular coil of wire with N turns is placed in a magnetic field that

Question

A loop rectangular coil of wire with N turns is placed in a magnetic field that is increasing in strength as B(t) = gamma t where gamma is a constant and t is time. The loop is increasing in size along both dimensions according to the functions w(t) = bt and l(t) = ct^2 where b and c are constants, w(t) is the width, and l(t) is the length. This problem may not be worked with motional emf because the field is changing c is just a constant, not the speed of light in this problem. gamma, b, and c are positive. (a) Compute the magnetic flux as a function of time. (b) Compute the induced emf. (c) Indicate the direction of the induced current flow on the diagram. Justify your choice of direction.

Explanation / Answer

(A) magnetic flux = N ( B . A )

= N ( y t) ( b t) (c t^2)

= N y b c t^4

(B) induced emf = d(flux) / dt

e = 4 N y b c t^3

(C) field is in out of the page direction and flux is increasing.

so current will such that field due to this induced current will be into the page.

so current will flow clockwise direction.

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