A coil of wire enclosing an area 100 cm2 is placed with its plane making an angle 60º with the magnetic field ofstrength 10-1T. What is the flux through the coil? If magnetic field is reduced to zero in 10-3 s, then find the inducedemf
Question
A coil of wire enclosing an area 100 cm2 is placed with its plane making an angle 60º with the magnetic field ofstrength 10-1T. What is the flux through the coil? If magnetic field is reduced to zero in 10-3 s, then find the inducedemf
Solution
The magnetic flux (Φ) through a coil is given by the formula:
Φ = B * A * cos(θ)
where: B is the magnetic field strength, A is the area enclosed by the coil, and θ is the angle between the magnetic field and the normal (perpendicular) to the coil.
Given: B = 10^-1 T (Tesla), A = 100 cm^2 = 100 * 10^-4 m^2 (converting cm^2 to m^2), and θ = 60 degrees.
Substituting these values into the formula, we get:
Φ = 10^-1 T * 100 * 10^-4 m^2 * cos(60) = 10^-1 T * 10^-2 m^2 * (1/2) (since cos(60) = 1/2) = 5 * 10^-4 Wb (Weber).
Next, the induced emf (ε) in a coil when the magnetic field changes is given by Faraday's law of electromagnetic induction, which states:
ε = -dΦ/dt
where: dΦ is the change in magnetic flux, and dt is the change in time.
Given: dΦ = Φ - 0 = 5 * 10^-4 Wb - 0 = 5 * 10^-4 Wb (since the magnetic field is reduced to zero), and dt = 10^-3 s.
Substituting these values into the formula, we get:
ε = -5 * 10^-4 Wb / 10^-3 s = -0.5 V.
The negative sign indicates that the induced emf opposes the change in magnetic flux, as per Lenz's law. However, in terms of magnitude, the induced emf is 0.5 V.
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