A small, circular washer of radius a = 0.750 cm is held directly below a long, straight wire carrying a current of I = 13.0 A. The washer is located h = 0.495 m above the top of a table (see figure below). Assume the magnetic field is nearly constant over the area of the washer and equal to the magnetic field at the center of the washer.
To calculate the magnetic field at the center of the washer due to the current-carrying wire, you can use the Biot-Savart law. The Biot-Savart law states that the magnetic field at a point due to a small segment of current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
The formula for the magnetic field at the center of the washer is given by:
B = (μ0 * I) / (2 * π * r)
Where:
- B is the magnetic field at the center of the washer
- μ0 is the permeability of free space, which is a constant equal to 4π x 10^(-7) Tm/A
- I is the current in the wire
- r is the distance between the wire and the center of the washer
In this case, the current (I) is given as 13.0 A and the radius (r) of the washer is 0.750 cm or 0.0075 m. The distance between the wire and the center of the washer is h, which is given as 0.495 m.
Plugging the values into the formula, we get:
B = (4π x 10^(-7) Tm/A * 13.0 A) / (2π * 0.0075 m)
Simplifying the expression:
B = (4π * 13.0 * 10^(-7)) / (2π * 0.0075) T
B = (52π x 10^(-7)) / (2π * 0.0075) T
Now, we can divide the common factors:
B = 52 x 10^(-7) / 0.015 T
B = 3466.66667 T
Therefore, the magnetic field at the center of the washer due to the current-carrying wire is approximately 3466.67 T.