Electric field and potential: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y) = 2xy – x2 – y, where x and y are measured in meters and V is in volts. At which point is the electric field equal to zero?

Induced electric fields: For a long ideal solenoid having a circular cross-section, the magnetic field strength within the solenoid is given by the equation B(t) = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid, find the radius of the solenoid.

Lenz’s law: A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the direction of the induced current in this coil as the field fades?

Camera: The focal length of a thin lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

Electromagnetic waves: An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

Snell’s law: A ray of light goes from one transparent material into another, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Electric field and potential: If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.

Ampere’s law: A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be

Internal battery resistance: The emf and the internal resistance of a battery are shown in the figure. If a current of 7.8 A is established through the battery from b to a, what is the terminal voltage Vab of the battery?

Ampere’s law: A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?