1.

The figure above shows a thin, square, nonconducting sheet of positive charge uniformly distributed over its area. The length of each side of the sheet is a. Point C is at the center of the sheet. Point X is a distanced above the center of the sheet, and point Y is a distance 2d above the center of the sheet. Assume a>>d. The effect of gravity is negligible.

1·If the magnitude of the electric field at point X is E，what is the magnitude of the electric field at point Y?

2. A positive point charge +q is released from rest at point X. If the magnitude of the electric field at point X is E，what is the kinetic energy of the charge at point Y?

3.

Capacitors C₁ and C₂ are connected as shown in the circuit above. The capacitance of C₁ is C/3，and the capacitance ofC2 is C/3. The equivalent capacitance between points A and B is C_EQ，A dielectric is inserted into capacitor C₂，and the equivalent capacitance between points A and B is now2C_EQ what is the value of the dielectric constant for this dielectric？

4. which of the following could be true for a Gaussian surface through which the net flux is zero?

5. A square coil with sides of length 1·0 cm is moved through a region of uniform magnetic field at a constant speed，as shown in the figure above. which of the following graphs best shows the current I in the coil as a function of  the position x of the right edge as the coil moves through the magnetic field，where counterclockwise current is positive?

6.

The y-component of the magnetic field B is given as a function of time t by the equation B_y=-α+βt，where α =4.0 T and β=3.0 T/s. A coil of wire with an area of 2.0 m² and a resistance of 6.0 Ω is placed in this field，parallel to the xz-·plane at y=2.0 cm. The current in the coil at time t=1.2 s is most nearly

7.

An inductor with inductance L=0.30 H is connected in series with a resistor and both are connected to a power supply, as shown above. The power supply generates a current I that is given as a function of time t by the equation I = I₀（1 -t/k）,where I₀ = 4.0 A and k=2.0 s，what is the magnitude of the potential difference across the inductor induced by the changing current?

8. A parallel plate capacitor with air between the plates is charged and then disconnected from the source of emf. If the space between the plates is now filled with a dielectric，what happens to the capacitance of the capacitor and the magnitude of the electric field between the plates？

9.

Questions9·11

The figure above shows two charged spherical conductors，X and Y，which are equal in size. When each conductor is isolated and surrounded by a closed cubical surface, the total electric flux through the surfaces is +Φ₀ for conductor X and -4Φ ₀ for conductor Y.

Conductor Y is brought into contact with conductor X and then separated. If the separation is small so that both conductors are inside the same closed cubical surface，as shown above what is the total electric flux through the surface?

10.

After being brought into contact with conductor X，conductor Y is moved a very large distance away from conductor X. What is  the total electric flux through a closed cubical surface surrounding conductor X，as shown above?

11.

Conductor Y is then moved closer to conductor X until it is just outside a closed cubical surface containing conductor X，as shown in the figure above. How would the total electric flux through the cubical surface change as conductor Y is moving?

12.

13. which of the following will increase the magnetic field on the axis of along solenoid? I. Increasing the current in the solenoid II. Increasing the cross-sectional area of the solenoid lll. Inserting an iron core into the solenoid

14.

Three long wires,R,S,and T，are in the positions and carrying the currents indicated in the figure above. AII currents are in the plane of the page and in the direction indicated. What are the magnitude and direction of the magnetic field at the origin?

Magnitude                    Direction