Question

A primary electromagnetic field (\( H_P \)) is being generated from current \( I_P \) flowing in a coil A with negligible capacitance, such that \( H_P = K I_P \sin \omega t \), where \( \omega \) is the angular frequency, \( K \) is a constant and \( t \) is time. A secondary electromagnetic field is being produced by induction in a conducting coil B. The phase difference between the primary and the secondary electromagnetic fields depends on which of the following factors?

• A. Inductance of coil B
• B. Resistance of coil B
• C. Frequency of the primary electromagnetic field
• D. Total current (\( I_P \)) flowing through the coil A

Hint:

The phase difference in electromagnetic induction setups typically depends on the inductance and resistance of the receiving coil and the frequency of the inducing signal.

Answer 1

The Correct Option is A, B, C

Step 1: Understand induced current and phase shift.
In electromagnetic induction methods, the primary coil generates a time-varying magnetic field, which induces an electromotive force (EMF) in the secondary coil (coil B). The current induced in coil B gives rise to the secondary field. The phase shift between the primary and secondary fields is influenced by how coil B responds to this induced EMF, which depends on its electrical impedance.

Step 2: Impedance and phase shift.
The impedance \( Z \) of coil B has both resistive and inductive components, and the phase angle \( \phi \) between the voltage and current is given by:
\[ \tan \phi = \frac{\omega L}{R} \] where:
    \( \omega \) = angular frequency
    \( L \) = inductance of the coil
    \( R \) = resistance of the coil

This implies that the phase shift is controlled by all three parameters: \( \omega \), \( L \), and \( R \).

Step 3: Role of total current \( I_P \).
While the magnitude of the primary field depends on the total current \( I_P \) flowing through the primary coil, the phase shift in the secondary field is determined by the impedance of coil B and the frequency. Hence, \( I_P \) does not directly control the phase shift. Option (D) is incorrect.

Final Answer:
Correct options: (A), (B), and (C)