A coil of area A = 0.25 m2 is rotating with angular speed ω = 380 rad/s with the axis of rotation perpendicular to a B = 0.55 T magnetic field. The coil has N = 550 turns. Part (a) Express the maximum emf induced in the loop, ε0, in terms of A, ω, B, and N. Part (b) Calculate the numerical value of ε0 in V.
A coil of area A = 0.25 m2 is rotating with angular speed ω = 380 rad/s with the axis of rotation perpendicular to a B = 0.55 T magnetic field. The coil has N = 550 turns. Part (a) Express the maximum emf induced in the loop, ε0, in terms of A, ω, B, and N. Part (b) Calculate the numerical value of ε0 in V.
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A coil of area A = 0.25 m2 is rotating with angular speed ω = 380 rad/s with the axis of rotation perpendicular to a B = 0.55 T magnetic field. The coil has N = 550 turns.
| Part (a) Express the maximum emf induced in the loop, ε0, in terms of A, ω, B, and N. |
| Part (b) Calculate the numerical value of ε0 in V. |
Transcribed Image Text:**Magnetic Induction in a Rotating Coil**
The image depicts a rotating cylindrical coil in a uniform magnetic field. Key components of the diagram include:
1. **Coil**: The cylindrical coil is shown as a series of concentric circles. It represents a coil of wire which can rotate around its axis.
2. **Rotation (\(\omega\))**: An arrow with the symbol \(\omega\) indicates the angular velocity, showing that the coil is rotating in a clockwise direction.
3. **Magnetic Field (\(\mathbf{B}\))**: The arrows labeled \(\mathbf{B}\) on both sides of the coil represent the direction and uniform nature of the magnetic field. The field is horizontal, with lines parallel to the axis of rotation.
**Explanation**: When the coil rotates in the magnetic field, it experiences a change in magnetic flux, inducing an electromotive force (EMF) due to electromagnetic induction, as per Faraday’s Law. This setup is the basis for devices like electric generators, where mechanical energy is converted into electrical energy.
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