Derive an expression for the magnetic field at the center of a solenoid with N turns (or loops) of wire, length L, and current I. If the length of the solenoid is much greater than its radius R, show that the magnetic field at the center is
A proton is at the origin and is moving in the +y direction with a speed of m/s, as shown below. What is the magnetic field at each of the points shown? Note: the points are symmetric, the distance between points C and E is , and the distance between points B and C is .
A dipole magnet and compass are arranged as shown below, with the dipole aligned East-West with the compass. The dipole moment of the magnet is and its center is 20 cm from the center of a compass. The magnetic field of Earth is shown.
A 1.5 V battery is connected to two copper wires that are connected together in series, as shown below. Wire 1 has a diameter of 1 mm and a length of 0.5 m. Wire 2 has a diameter of 2 mm and the same length as Wire 1. The mobile electron density of copper n is , and the electron mobility in copper u is .
An RC circuit has a 6-V battery, a resistor, and a capacitor. At , there is no charge on the capacitor plates. At , the switch is closed, and the capacitor begins to charge.