Find the magnetic flux through a circular loop 6.0 cm in diameter oriented with the loop normal at 50 degrees to a uniform 60 mT magnetic field.
To find the magnetic flux through a circular loop, we can use the formula:
Φ = B * A * cos(theta)
Where:
- Φ is the magnetic flux
- B is the magnetic field strength
- A is the area of the loop
- theta is the angle between the normal of the loop and the magnetic field direction
Step 1: Calculate the area of the circular loop
The formula to calculate the area of a circle is:
A = π * r^2
Given that the diameter of the circular loop is 6.0 cm, we can calculate the radius as:
r = diameter / 2 = 6.0 cm / 2 = 3.0 cm = 0.03 m
Now, we can calculate the area as:
A = π * (0.03 m)^2
Step 2: Calculate the angle between the loop normal and the magnetic field direction
Given that the loop normal is oriented at an angle of 50 degrees to the magnetic field, we have:
theta = 50 degrees
Step 3: Substitute the values into the formula and calculate the magnetic flux
Given that the magnetic field strength is 60 mT, we convert it to SI units (T):
B = 60 mT = 60 x 10^-3 T = 0.06 T
Now, substitute the values into the formula:
Φ = B * A * cos(theta)
= 0.06 T * [(π * (0.03 m)^2)] * cos(50 degrees)
Calculating this value will give you the magnetic flux through the circular loop.