Question

The total charge, induced in a conducting loop when it is moved in magnetic field depend on

• A. the rate of change of magnetic flux
• B. initial magnetic flux only
• C. the total change in magnetic flux
• D. final magnetic flux only

Answer 1

The Correct Option is C

To determine the total charge induced in a conducting loop moving through a magnetic field, we need to understand the concept of electromagnetic induction, which is principally described by Faraday's Law of Electromagnetic Induction.

According to Faraday's Law, the induced electromotive force (emf) in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. Mathematically, it is expressed as:

\text{EMF} = - \frac{d\Phi_B}{dt}

Where:

• \Phi_B is the magnetic flux,
• t is the time.

The magnetic flux \Phi_B is given by:

\Phi_B = B \cdot A \cdot \cos(\theta)

Where:

• B is the magnetic field strength,
• A is the area vector perpendicular to the field, and
• \theta is the angle between the magnetic field and the normal to the area.

In a scenario where the conducting loop is moved such that the magnetic field changes, the total induced charge Q can be calculated as:

Q = \frac{\text{total change in flux}}{R}

Where R is the resistance of the loop. This implies that the induced charge is directly proportional to the total change in magnetic flux, not just the rate of change, initial, or final flux.

Therefore, the correct answer is: the total change in magnetic flux.

Let's rule out the other options:

• The rate of change of magnetic flux: This is associated with the induced emf, but it doesn't directly determine the total charge induced.
• Initial magnetic flux only: The initial magnetic flux doesn't provide information on the total change unless compared with a final state, making it insufficient alone.
• Final magnetic flux only: Similar to the initial flux, the final flux alone doesn't account for the total change without the initial state.

Hence, the answer correctly identifies the dependency on the total change in magnetic flux for the induced charge.