A conducting loop in the form of a circle placed perpendicular to a magnetic field of 0.40 T. If the area of the loop increases at m^2/s, what is the induced emf in the loop?
To determine the induced emf in the loop, you can use Faraday's Law of electromagnetic induction. This law states that the induced emf is equal to the rate of change of magnetic flux through the loop.
The magnetic flux (Φ) through the loop is given by the equation Φ = B * A, where B is the magnetic field strength (0.40 T) and A is the area of the loop.
Since the area of the loop is increasing at a rate of m^2/s, the rate of change of area (dA/dt) is equal to this value. So, dA/dt = m^2/s.
Now, we can calculate the induced emf using the formula:
emf = -N * dΦ/dt
Where N represents the number of turns in the loop, which in this case is 1. Since we are only dealing with a single loop, N = 1.
First, we find the rate of change of magnetic flux (dΦ/dt). Since Φ = B * A, we have:
dΦ/dt = d(B * A)/dt = B * dA/dt = B * (m^2/s)
Finally, we substitute the values into the formula for emf:
emf = -N * dΦ/dt = -(1) * (B * (m^2/s)) = -B * (m^2/s)
The induced emf in the loop is equal to -B * (m^2/s). Note the negative sign indicates the direction of the induced current, according to Lenz's Law.
To find the induced emf in the loop, we can use Faraday's law of electromagnetic induction:
EMF = -Rate of change of magnetic flux
The magnetic flux, Φ, is given by the product of magnetic field, B, and the area, A, enclosed by the loop:
Φ = B * A
Given that the magnetic field, B, is 0.40 T, and the area, A, is increasing at a rate of dA/dt = m^2/s, we can substitute these values into the equation to find the rate of change of magnetic flux:
dΦ/dt = B * dA/dt
dΦ/dt = 0.40 T * (m^2/s)
Now, the induced emf is equal to the negative rate of change of magnetic flux:
EMF = -dΦ/dt
Let's substitute the values:
EMF = - (0.40 T * (m^2/s))
Therefore, the induced emf in the loop is -0.40 T * (m^2/s).