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

Figure: Solenoid

2h30001 Acceleration of an alpha particle by charged plates 2h30001

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 .

Figure: Find the magnetic field at various points around a moving charged particle.

2ha0001 Deflection of a compass needle by a dipole magnet 2ha0001

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.

Sketch and calculate the deflection of the compass needle from North.

If you replace the magnetic dipole with a thin coil of radius 2 cm and 20 turns at the same location, what must be the current in the coil to give the same deflection of the compass needle as the dipole magnet?

Figure: Dipole magnet and compass.

2ia0001 Potential difference, electric field, drift speed, and current for two wires connected in series. 2ia0001

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 .

Figure: Circuit with a battery and two copper wires of different diameters connected in series.

What is the potential difference across each wire?

What is the electric field in each wire?

What is the drift speed of mobile electrons in each wire?

What is the current through each wire?

2jg0001 Charging Capacitor in an RC circuit 2jg0001

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.

Figure: RC Circuit

What is the time constant of the charging capacitor?

Sketch graphs of vs. , vs. , vs. , and vs. .

At , what is , , , and ?

Sketch the charge on the capacitor plates at .

Sketch due to surface charge on the wire at point P at .

Sketch the fringe field due to surface charge on the capacitor plates, at point P at .