Question

A straight wire carrying a current of \(3.41 \mathrm{~A}\) is placed at an angle of \(10.0^{\circ}\) to the horizontal between the pole tips of a magnet producing a field of 0.220 T upward. The poles' tips each have a \(10.0 \mathrm{~cm}\) diameter. The magnetic force causes the wire to move out of the space between the poles. What is the magnitude of that force?

Short answer

Answer: To calculate the magnetic force on the wire, we first determine the length of the wire exposed to the magnetic field using the diameter of the pole tips and the angle between the wire and the horizontal: L = D*cos(10.0°). Then, we use the formula F = BIL*sin(θ) to find the magnitude of the magnetic force on the wire.

Step-by-step solution

Identify the given values

We are given the following values: - Current (\(I\)) in the wire: \(3.41 \mathrm{A}\) - Angle (\(\theta\)) between the wire and the horizontal: \(10.0^{\circ}\) - Magnetic field strength (\(B\)): \(0.22 \mathrm{T}\) - Pole tip diameter (\(D\)): \(10.0 \mathrm{cm}\) or \(0.1 \mathrm{m}\)

Calculate the length of the wire exposed to the magnetic field

We need to find the length of the wire (\(L\)) exposed to the magnetic field. This can be calculated by using the diameter of the pole tips and the angle between the wire and the horizontal: \(L = D \cos{\theta}\) First, convert the angle from degrees to radians: \(\theta_{rad} = 10.0^{\circ} \cdot \frac{\pi}{180^{\circ}}\) Now, the length \(L\) of the wire exposed to the magnetic field can be determined: \(L = 0.1 \mathrm{m} \cdot \cos{(10.0^{\circ})}\)

Calculate the magnetic force on the wire

To calculate the magnetic force on the wire, we can use the formula: \(F = BIL\sin{\theta}\) Inputting our given values and calculated wire length \(L\), we get: \(F = (0.22 \mathrm{T}) \cdot (3.41 \mathrm{A}) \cdot L \sin{(10.0^{\circ})}\) Finally, calculate the force \(F\) to find the magnitude of the magnetic force on the wire. Remember that the final units for force will be Newtons (N).