Question

On what factors does the magnetic flux linked with a coil depend? Explain the induced electromotive force on the basis of the following:
(i) Cause
(ii) Magnitude
(iii) Direction

Hint:

Remember, a change in flux induces an EMF that opposes the cause producing it.

Answer 1

Step 1: Magnetic flux (\( \Phi \)) linked with a coil depends on: \[ \Phi = B A \cos \theta \] where:
- \( B \) = Magnetic field strength
- \( A \) = Area of the coil
- \( \theta \) = Angle between the field and the normal to the coil \[ \boxed{\text{Flux depends on } B, A, \text{ and } \theta.} \]

 (i) Cause
 Solution: The changing magnetic field causes an induced electromotive force (EMF). 

Step 1: According to Faraday's law, EMF is induced when the magnetic flux through a coil changes with time. \[ \mathcal{E} = -\frac{d\Phi}{dt} \] \[ \boxed{\text{Changing flux induces EMF.}} \] 

(ii) Magnitude
Solution: The magnitude of induced EMF is proportional to the rate of change of flux. 

Step 1: Using Faraday's law, the magnitude of the induced EMF is: \[ |\mathcal{E}| = \left| \frac{d\Phi}{dt} \right| \] 

Step 2: Faster changes in flux result in higher EMF. \[ \boxed{\mathcal{E} \propto \frac{d\Phi}{dt}} \] 

(iii) Direction
Solution: The direction of induced EMF is given by Lenz's Law. 

Step 1: According to Lenz's Law, the induced EMF opposes the change in magnetic flux. 

Step 2: The negative sign in Faraday's law signifies this opposition. \[ \mathcal{E} = -\frac{d\Phi}{dt} \] \[ \boxed{\text{Opposes the flux change.}} \]