A rectangular wire loop of dimensions a×b, with a=3.5 cm and b=4.5 cm, is pulled parallel to side a at a constant speed v=4.3 m/sec into a region where the magnetic field, |B|=0.125 T, is uniform and perpendicular to the loop. The loop enters the magnetic field at time t=0.

(a) Calculate the rate at which the magnetic flux through the loop is changing. Express your answer in Tesla m2/sec.

(b) What is the magnitude of the induced EMF at time t?

ℰ=-dΦ/dt=-d( BAcosα )/dt

cosα=1
ℰ =BA/t= Bab/t=Bb(a/t)=Bbv=
=0.125•0.045•4.3=0.024 V

what is the rate? ._.

both a) and b) are 0.024

To find the rate at which the magnetic flux through the loop is changing, we need to understand the equation for magnetic flux and how it changes with time.

(a) The magnetic flux (Φ) through a loop of wire is given by the equation Φ = B * A * cosθ, where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field and the surface normal of the loop.

In this case, the magnetic field is perpendicular to the loop, so cosθ = 1. The area of the loop (A) is given by the product of its dimensions, A = a * b.

We are given the values for a = 3.5 cm (0.035 m) and b = 4.5 cm (0.045 m), and the magnetic field strength |B| = 0.125 T.

The rate at which the magnetic flux through the loop is changing can be found using the equation:

dΦ/dt = B * dA/dt * cosθ

Since the loop is being pulled parallel to side a, the area of the loop changes with time, but the angle between the magnetic field and the surface normal remains constant at 90 degrees (perpendicular).

The rate at which the area A changes with time can be found using the equation:

dA/dt = v * b

where v is the constant speed at which the loop is being pulled into the magnetic field, and b is the dimension of the loop perpendicular to its motion.

Plugging in the given values, we have:

dA/dt = (4.3 m/s) * (0.045 m)

dA/dt = 0.1935 m2/s

Now, we can calculate the rate at which the magnetic flux through the loop is changing:

dΦ/dt = (0.125 T) * (0.1935 m2/s) * (1)

dΦ/dt = 0.02419 T·m2/s

Therefore, the rate at which the magnetic flux through the loop is changing is 0.02419 Tesla m2/sec.

(b) The magnitude of the induced electromotive force (EMF) at time t can be found using Faraday's law of electromagnetic induction. It states that the induced EMF (ε) in a loop of wire is equal to the rate of change of magnetic flux through the loop.

Mathematically, we have:

ε = - dΦ/dt

Plugging in the value we calculated for dΦ/dt, we get:

ε = - 0.02419 T·m2/s

Therefore, the magnitude of the induced EMF at time t is 0.02419 V (Volts). Note that the negative sign indicates that the direction of the induced current is opposite to the change in flux.