consider a flat square coil with 10 turns. The coil is 1m wide on each side and has a magnetic field of 1,0T passing through it. The plane of the coil is perpendicular to the magnetic field: the field points out of the page. Use faraday's law to calculate the induced emf, if the magnetic field is increased uniformly from 1,0 T to 2 T in 20s working : width 1mX10 turns=10. 10x1,0=10. ,
To calculate the induced emf using Faraday's law, we need to find the rate of change of magnetic flux through the coil.
The magnetic flux through a coil is given by the formula:
Φ = B * A * cos(θ)
where:
- Φ is the magnetic flux
- B is the magnetic field
- A is the area of the coil
- θ is the angle between the magnetic field and the normal to the coil's surface
In this case, since the magnetic field is perpendicular to the coil (θ = 0), the formula simplifies to:
Φ = B * A
Given that the magnetic field is initially 1.0 T and increases to 2 T, and the area of the coil is 1m x 1m = 1 m², we can calculate the change in magnetic flux:
ΔΦ = (2 T * 1 m²) - (1.0 T * 1 m²)
= 2 T * 1 m² - 1.0 T * 1 m²
= 2 T * 1 m² - 1.0 T * 1 m²
= 1 T * 1 m²
So, the change in magnetic flux is 1 T * 1 m² = 1 T·m².
Now, we need to calculate the time rate of change of magnetic flux (dΦ/dt), which gives us the induced emf (ε) according to Faraday's law:
ε = - dΦ/dt
Given that the change in magnetic field occurs uniformly over 20 seconds, we can calculate the time rate of change of magnetic flux:
dΦ/dt = ΔΦ / Δt
= 1 T·m² / 20 s
= 0.05 T·m²/s
Therefore, the induced emf is equal to:
ε = - dΦ/dt
= - 0.05 T·m²/s
Note: The negative sign indicates that the direction of the induced emf is opposing the change in magnetic field.
To calculate the induced emf using Faraday's law, you need to follow these steps:
1. Determine the change in magnetic field (ΔB) over the given time period. In this case, the magnetic field increases from 1.0 T to 2.0 T, so ΔB = 2.0 T - 1.0 T = 1.0 T.
2. Calculate the area of the square coil. The width is given as 1 m, and there are 10 turns, so the total width of the coil is 1 m x 10 turns = 10 m.
3. Use this width to calculate the area (A) of the coil. The area of a square is given by A = length x width, and since it is a square with sides measuring 1 m, length = width = 1 m. So, A = 1 m x 1 m = 1 m².
4. Apply Faraday's law to calculate the induced emf (ε):
ε = -ΔB / Δt x A,
where Δt is the time interval over which the magnetic field changes. In this case, Δt = 20 s.
Therefore, ε = -1.0 T / 20 s x 1 m² = -0.05 V.
The negative sign indicates that the induced emf creates a current that opposes the change in the magnetic field. So, the magnitude of the induced emf is 0.05 V.