Given:
- Diameter of the circular ring = 20 cm
- Resistance of the ring = 0.01 Ω
- Magnetic field = 2 T

To find:
- The amount of charge that flows through the ring when it is rotated from a position perpendicular to the magnetic field to a position parallel to the field

Explanation:
The amount of charge that flows through a conductor can be determined using the formula:

Q = I * t

Where:
Q is the charge (in coulombs),
I is the current (in amperes), and
t is the time (in seconds).

In this case, we need to find the current flowing through the ring and the time taken for the rotation.

Step 1: Calculate the current:
The current can be calculated using Ohm's Law:

I = V / R

Where:
I is the current (in amperes),
V is the voltage (in volts), and
R is the resistance (in ohms).

In this case, the voltage can be determined using the formula:

V = B * A * ω

Where:
V is the voltage (in volts),
B is the magnetic field (in teslas),
A is the area (in square meters), and
ω is the angular velocity (in radians per second).

Step 2: Calculate the area:
The area of the circular ring can be determined using the formula:

A = π * r^2

Where:
A is the area (in square meters), and
r is the radius (in meters).

In this case, the radius can be determined using the formula:

r = d / 2

Where:
r is the radius (in meters),
d is the diameter (in meters).

Step 3: Calculate the angular velocity:
The angular velocity can be determined using the formula:

ω = θ / t

Where:
ω is the angular velocity (in radians per second),
θ is the angle of rotation (in radians), and
t is the time taken for rotation (in seconds).

In this case, the angle of rotation is 90 degrees or π/2 radians.

Step 4: Calculate the time:
The time taken for rotation can be determined using the formula:

t = θ / ω

Where:
t is the time taken for rotation (in seconds),
θ is the angle of rotation (in radians), and
ω is the angular velocity (in radians per second).

Step 5: Calculate the charge:
Using the calculated values of current and time, we can now determine the charge flowing through the ring using the formula:

Q = I * t

Calculation:
Step 1: Calculate the current
- Given: R = 0.01 Ω
- We know that V = B * A * ω
- Given: B = 2 T
- Let's calculate A first
- Given: d = 20 cm = 0.2 m
- We know that A = π * r^2
- Calculating r: r = d / 2 = 0.1 m
- Substituting the values, A = π * (0.1)^2 = 0.01 * π m^2
- Now