A rectangular loop (a = 0.20 m, b = 0.40 m) is pushed into a space where there i

Question

A rectangular loop (a = 0.20 m, b = 0.40 m) is pushed into a space where there is uniform magnetic field with a speed of 3.80 m/s.
a) What is the induced current in the rod if the magnetic field is uniform and has a magnitude of 5.00 T, and the resistance of the loop is 75.0 ??
Amp

A rectangular loop (a = 0.20 m, b = 0.40 m) is pushed into a space where there is uniform magnetic field with a speed of 3.80 m/s. a) What is the induced current in the rod if the magnetic field is uniform and has a magnitude of 5.00 T, and the resistance of the loop is 75.0 ?? Amp

Explanation / Answer

Because the loop is pushed into de space with magnetic field, there is a part of the loop outside from that space, let's call X to that part of the loop, so, there is an area (a-X)b inside the field an area Xb outside.

Since the magnetic field is uniform and constante (in the reigion where it exists), the Magnetic field flux will be

Phi = B (a-X)b

B, a and b are constant, so the inducted FEM (E) will be (Faraday's Law):

E = -d(Phi)/dt = -d(B (a-X)b)/dt = - Bb (-dx/dt) = -Bb v        (-dx/dt is the loop's speed)

I = E/R = -Bbv/R   (the - sign implies tha the curren will produce a magneic field opposite to th e flux change)

I = 0.101 Amp

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