Review 1

Example1: Three point charges are arranged as shown Example1: Three point charges are arranged as shown. a) Find the vector electric field that the 6.00-nC and –3.00-nC charges together create at the origin. b) Find the vector force on the 5.00-nC charge.

Solution

Example2: Two point charges each of magnitude 2 Example2: Two point charges each of magnitude 2.00 μC are located on the x axis. One is at x = 1.00 m, and the other is at x = ‑1.00 m. a) Determine the electric potential on the y axis at y = 0.500 m. b) Calculate the change in electric potential energy of the system as a third charge of –3.00 μC is brought from infinitely far away to a position on the y axis at y = 0.500 m.

Solution

Example3: Consider a series RC circuit for which R = 1. 00 MΩ, C = 5 Example3: Consider a series RC circuit for which R = 1.00 MΩ, C = 5.00 μF, and ε = 30.0 V. Find a) the time constant of the circuit and b) the maximum charge on the capacitor after the switch is closed. c) Find the current in the resistor 10.0 s after the switch is closed.

Solution

Example4: A rectangular coil consists of N =100 closely wrapped turns and has dimensions a=0.400m and b=0.300m. The coil is hinged along the y axis, and its plane makes an angle θ=30.0° with the x axis. What is the magnitude of the torque exerted on the coil by a uniform magnetic field B=0.800 T directed along the x axis when the current is I=1.20 A in the direction shown? What is the expected direction of rotation of the coil?

Solution

Example5: Two long, parallel conductors carry currents I1 = 3 Example5: Two long, parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A, both directed into the page in figure below. Determine the magnitude and direction of the resultant magnetic field at P.

Solution

Example6: A circular loop of wire of radius r is in a uniform magnetic field, with the plane of the loop perpendicular to the direction of the field. The magnetic field varies with time according to B(t) = a + bt, where a and b are constants. a) Calculate the magnetic flux through the loop at t = 0. b) Calculate the emf induced in the loop. c) If the resistance of the loop is R, what is the induced current? d) At what rate is energy being delivered to the resistance of the loop?

Solution

Example7: An inductor that has an inductance of 15 Example7: An inductor that has an inductance of 15.0 H and a resistance of 30.0 Ω is connected across a 100-V battery. What is the rate of increase of the current a) at t = 0 and b) at t = 1.50 s?

Solution