A coil of wire is arranged with its plane perpendicular to a uniform magnetic field with flux density B. When the radius of the coil increases from r₁ to r₂ in time At, then what is the emf induced in the coil?
Correct answer: A. πB(r2-r2)/Δt
- A. πB(r2-r2)/Δt
- B. πB(r2-r2)2/Δt
- C. B(r2-r2)/Δt
- D. B(r2+r2)/Δt
Explanation
The induced electromotive force (EMF) in a coil with a changing area in a magnetic field is given by Faraday's law as EMF =- Δ/Δt.where Δ is the change in magnetic flux. The magnetic flux (4) through the coil is given by B. A, where B is the magnetic flux density, and A is the area of the coil.The area of the coil is proportional to r² (assuming a circular coil), so the change in area AA when the radius changes from r₁ to rais (rri).Therefore, the induced EMF (EMF) is given by:EMF - Δ/Δt = - BΔA/Δt = πB(r2-r2)/ΔtTherefore, the correct option is (a))πB(r2-r2)/Δt
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About Electromagnetism
Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.
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