A rectangular wire loop (dimensions of h = 30.0 cm and w = 14.00 cm) with resist

Question

A rectangular wire loop (dimensions of h = 30.0 cm and w = 14.00 cm) with resistance R = 5.00 O is mounted on a door. The Earth's magnetic field, BE = 2.6 10-5 T, is uniform and perpendicular to the surface of the closed door (the surface is in the xz-plane). At time t = 0, the door is opened (right edge moves toward the y-axis) at a constant rate, with an opening angle of ?(t) = ?t, where ? = 2.6 rad/s. Calculate the direction and the magnitude of the current induced in the loop, i(t = 0.200 s).

Relevant images:
http://www.webassign.net/bauerphys1/29-p-072a.gif
http://www.webassign.net/bauerphys1/29-p-072b.gif

The answer should be 282 nA in a clockwise direction, but how do I obtain this answer?

Explanation / Answer

A rectangular wire loop dimensions are h = 30.0cm , w = 14.00cm Area of the rectangular loop wire is A = 30.0cm * 14.0cm                                                              = 0.042m^2 The earths magnetic field is B = 2.6*10^-5 T angular frequency is = 2.6 rad /s    induced emf is e = N B A sint                                = 2.6*10^-5 T * 0.042m^2 * 2.6 rad/ s sin ( 2.6 rad /s * 0.200s)                                = 2.57*10^-8 V induced current is   I = e / R                                    = 2.57*10^-8 V / 5.00                                    = 5.15*10^-9 A

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