A wire loop has an area of 0.12 m2, and the magnetic field through it increases from 0 to 0.20 T in 0.30 s. What is the induced emf in the loop?
ε = - dΦ/dt =- d(B•A•cosα)/dt.
If cos α =±1, then
ε =A•(Δ B/Δt) =
= A•(B2 –B1)/ Δt =
= 0.12•0.2/0.3 =0.08 V
To find the induced emf in the loop, we can use Faraday's Law of electromagnetic induction, which states that the emf (𝐸) induced in a wire loop is equal to the negative rate of change of magnetic flux through the loop.
The magnetic flux (𝜙) through a wire loop is given by the formula:
𝜙 = 𝐵𝐴
Where:
- 𝜙 is the magnetic flux.
- 𝐵 is the magnetic field.
- 𝐴 is the area of the loop.
In this case, the area of the loop is given as 0.12 m^2, and the magnetic field changes from 0 to 0.20 T. Therefore, the change in magnetic flux (∆𝜙) can be calculated as:
∆𝜙 = 𝐵₂𝐴 - 𝐵₁𝐴 = (0.20 T)(0.12 m^2) - (0 T)(0.12 m^2) = 0.024 T·m²
The time taken for the change in magnetic field is given as 0.30 s.
Finally, using Faraday's Law, we can find the induced emf (𝐸) as:
𝐸 = -∆𝜙/∆𝑡
= -(0.024 T·m²)/(0.30 s)
= -0.08 V (where V represents volts)
Therefore, the induced emf in the loop is -0.08 V.
To find the induced emf in the loop, you can use Faraday's Law of electromagnetic induction, which states that the induced emf (ε) in a wire loop is proportional to the rate of change of magnetic flux through the loop.
The formula to calculate the induced emf is:
ε = -N * ΔΦ / Δt
Where:
- ε is the induced emf in volts (V).
- N is the number of turns in the wire loop.
- ΔΦ is the change in magnetic flux in webers (Wb).
- Δt is the change in time in seconds (s).
Given data:
- The area of the wire loop (A) = 0.12 m²
- The change in magnetic field (ΔB) = 0.20 T
- The change in time (Δt) = 0.30 s
First, we need to calculate the change in magnetic flux (ΔΦ) through the wire loop.
ΔΦ = B * A
Where:
- B is the magnetic field in teslas (T).
ΔΦ = 0.20 T * 0.12 m²
ΔΦ = 0.024 Wb
Now, we can substitute the values into the formula to calculate the induced emf (ε).
ε = -N * ΔΦ / Δt
Since we don't have the value of the number of turns (N), let's assume it's 1 for simplicity.
ε = -1 * 0.024 Wb / 0.30 s
ε = -0.08 V
The negative sign indicates that the direction of the induced current would be such that it opposes the change in magnetic field. Therefore, the induced emf in the loop is -0.08 V.