find the charge flown in loop if loop is rotated about axis AB by 90degree 180degree and 360degree

To determine the charge that flows in a loop when it is rotated about an axis, we need to consider the principles of electromagnetic induction, particularly Faraday's law of induction. This law states that a change in magnetic flux through a circuit induces an electromotive force (EMF) in the circuit, which can cause a current to flow if the circuit is closed. Let's break down the scenario where the loop is rotated by 90 degrees, 180 degrees, and 360 degrees.

Understanding the Setup

Imagine we have a circular loop of wire placed in a uniform magnetic field. The orientation of the loop relative to the magnetic field lines will determine the magnetic flux through the loop. The magnetic flux (Φ) is given by the formula:

Φ = B * A * cos(θ)

Where:

• B is the magnetic field strength.
• A is the area of the loop.
• θ is the angle between the magnetic field and the normal (perpendicular) to the loop's surface.

Charge Flow for Different Rotations

1. Rotation by 90 Degrees

When the loop is rotated by 90 degrees, the angle θ changes from 0 degrees (where the magnetic flux is maximum) to 90 degrees (where the magnetic flux is zero). The change in magnetic flux (ΔΦ) can be calculated as:

ΔΦ = Φ_final - Φ_initial = B * A * cos(90°) - B * A * cos(0°) = 0 - B * A = -B * A

This change in flux induces an EMF (ε) in the loop, given by:

ε = -dΦ/dt

Assuming the rotation happens in a time interval Δt, the induced EMF can be calculated. If the loop has a resistance (R), the current (I) flowing through the loop can be found using Ohm's law:

I = ε/R

The total charge (Q) that flows can then be calculated as:

Q = I * Δt

2. Rotation by 180 Degrees

For a 180-degree rotation, the loop moves from an orientation where the magnetic flux is maximum to the opposite orientation where the magnetic flux is also maximum but in the opposite direction. The change in flux is:

ΔΦ = B * A * cos(180°) - B * A * cos(0°) = -B * A - B * A = -2B * A

Following the same steps as before, the induced EMF will be:

ε = -dΦ/dt

And the charge that flows through the loop can be calculated similarly:

Q = I * Δt

3. Rotation by 360 Degrees

When the loop is rotated by 360 degrees, it returns to its original position. The change in magnetic flux is:

ΔΦ = B * A * cos(0°) - B * A * cos(0°) = B * A - B * A = 0

Since there is no change in flux, there is no induced EMF, and consequently, no current flows through the loop:

Q = 0

Summary of Charge Flow

In summary, the charge that flows in the loop when rotated about axis AB is:

• 90 degrees: A certain amount of charge flows, calculated based on the induced EMF.
• 180 degrees: A larger amount of charge flows due to a greater change in magnetic flux.
• 360 degrees: No charge flows since there is no change in magnetic flux.

This analysis illustrates the relationship between rotation, magnetic flux, and induced charge flow in a loop. Understanding these principles is crucial in fields such as electrical engineering and physics, particularly in applications involving generators and motors.