You decide to build a home-made potato gun based on the magnetic force. The design is as follows: two parallel rails, separated by a distance of 1 m, have an accelerating length of 10 m. Your load has a mass of 0.1 kg. The current running in the rails and through the load is 10 A, the magnetic field through the circuit is 0.1 T.
a) What is the required direction of the magnetic field?
b) What is the launch speed with which the load leaves the rails?
a) To determine the required direction of the magnetic field, we can use the right-hand rule for the force on a current-carrying wire in a magnetic field. If you point your right thumb in the direction of the current (from positive to negative), and your fingers in the direction of the magnetic field, then the palm of your hand will point in the direction of the force acting on the wire. In this case, the force needs to be directed upwards to accelerate the load, so the magnetic field should be directed into the page.
b) To calculate the launch speed of the load, we can use the formula for the force on a current-carrying wire in a magnetic field, which is given by:
F = ILB sin(theta)
Where:
F = force
I = current (10 A)
L = length of wire in the magnetic field (10 m)
B = magnetic field strength (0.1 T)
theta = angle between the current direction and the magnetic field direction
Since the angle is 90 degrees in this case, sin(theta) = 1. Therefore, the force on the load is:
F = 10 A * 10 m * 0.1 T = 10 N
This force will accelerate the load over a distance of 1 m, converting it to kinetic energy. We can calculate the velocity using the work done by the force:
KE = F * d
0.5 * m * v^2 = F * d
v = sqrt(2 * F * d / m)
Substitute in our values to find the launch speed:
v = sqrt(2 * 10 N * 1 m / 0.1 kg) = 14.1 m/s
Therefore, the launch speed of the load as it leaves the rails is 14.1 m/s.