A coil of 50 turns has a cross-sectional area of 4.2x10^-3 m^2. It is placed at an angle to a uniform magnetic field of flux density 2.8 x 10^-2 T, so that the angle = 50degrees. What is the change in flux linkage when the coil is rotated anticlockwise until angle = 0degree?
2.1 x 10^-3 Wb turns increase
To calculate the change in flux linkage when the coil is rotated, we need to use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) is equal to the rate of change of flux linkage.
The flux linkage (ϕ) is given by the formula:
ϕ = N * B * A * cos(θ)
Where:
N = number of turns in the coil (50 turns)
B = magnetic field flux density (2.8 x 10^-2 T)
A = cross-sectional area of the coil (4.2 x 10^-3 m^2)
θ = angle between the coil's normal and the magnetic field (50 degrees)
The change in flux linkage (∆ϕ) when the coil is rotated anticlockwise until θ = 0 degrees can be calculated by subtracting the initial flux linkage (∆ϕ_initial) from the final flux linkage (∆ϕ_final):
∆ϕ = ∆ϕ_final - ∆ϕ_initial
Now, let's calculate the initial and final flux linkages.
Initial Flux Linkage (∆ϕ_initial):
Using the given values:
∆ϕ_initial = N * B * A * cos(50 degrees)
Final Flux Linkage (∆ϕ_final):
When θ = 0 degrees, the cos(0) = 1. Therefore:
∆ϕ_final = N * B * A * cos(0 degrees)
Finally, we can calculate the change in flux linkage:
∆ϕ = ∆ϕ_final - ∆ϕ_initial
Please calculate the values to find the change in flux linkage.