Physics 212 – Midterm Exam I NAME:______________________

Summer 2003 STUDENT ID#:_______________

Prof. Milos Steinhart

INSTRUCTIONS: This is a closed book exam. You may use only the one page of formulas provided to you. You must show all of your work in the space provided for each question and you must include appropriate units and significant figures. If you need more space, use the other side of the paper but mark clearly to which problem and which question is your work related. Do not use other papers!

You are bound by the University’s Honor Code. Any evidence of cheating must be reported to the College of Arts and Sciences.

PLEASE CIRCLE ALL ANSWERS

All problems are worth 20 points. Partial credits are shown in brackets.

SCORE

Problem 1 _____________________

Problem 2 _____________________

Problem 3 _____________________

Problem 4 _____________________

Problem 5 _____________________

TOTAL _____________________

Problem 1: A spherical drop of water carrying a charge 30 pC has a potential of 500 V at its surface.

a) (5) What is the radius of the drop?

b) (5) What is the intensity of the electric field near to the surface of this drop?

c) (5) If eight such drops of the same charge and radius combine to form a big single spherical drop. What is the potential at its surface?

d) (5) What is the intensity of the electric field near to the surface of the big drop?

Problem 2: A slab of copper of thickness b is inserted into a parallel plate capacitor with the plates of the area A, separated by the distance d (of air). The capacitor is charged but the power source is disconnected before the insertion of the slab..

a) (6) What is the ratio of the capacitance before to that after the slab is inserted?

b) (6) Find the ratio of the stored energy before to that after the slab is inserted?

c) (6) How much work is done on the slab (by an external agent) when the slab is inserted?

d) (2) Is the slab pulled in by the field or do we (as the external agent) have to push it in?

Problem 3: At a certain time a charged particle with the mass of m = 20 ng (20 10^-12 kg) was detected in a point a of a uniform electrostatic field. The potential in the point a is j_a = 10⁵ V and the speed of the particle is v_a = 10⁵ m/s. Later the same particle was detected in a point b exactly 1 m to the right from the point a. The potential in the point b is j_b = 8 10⁴ V and the speed of the particle is v_b = 8 10⁴ m/s. The influence of gravitation can be neglected!

a) (4) Describe in detail the electrostatic field.

b) (8) What is the work done by the electric field on the particle?

c) (8) What is the charge of the particle?

Problem 4: We have a circuit:

a) (2) What is the topology of the circuit?

b) (5) What is the current in the point A (A hint: take care of resistors R₂ and R₃ first!)

c) (5) Find the potential in the points A, B, C, D with respect to the potential in the point E.

d) (4) How the current in the point A changes, if we change the V₁ from 24 V to 15 V?

e) (4) How this current changes, if we change V₁ back to 24 V and increase V₂ four times?

Problem 5: Multiple choice. Pick the single best answer to each conceptual question below. Please include a brief explanation for partial credit. Each answer is worth 4 pts.

1. An electric dipole in a uniform electrostatic field experiences

a) Only a net external force.

b) Only a torque.

c) Both a net external force and a torque.

d) Neither net external force nor a torque.

e) Answer depends on the strength of the field.

2. A spherical metal shell in equilibrium carries a uniform positive surface charge. The potential is the same over the surface of the shell. Which statement is correct?

a) The potential is the highest in the geometrical center of the shell.

b) The potential is the lowest in the geometrical center of the shell.

c) The potential at any point within the shell volume is the same as on the shell surface.

3. Compared with the applied electric field, the electric field within a linear dielectric is

a) Smaller.

b) Larger.

c) Depends on the dielectric.

d) The same.

4. Two identical capacitors are connected first in parallel and then in series. Which combination has the greatest capacitance?

a) The pair in parallel.

b) The pair in series.

c) The two combinations have the same capacitance.

5. Two identical resistors are connected first in parallel and then in series. Which combination has the greatest resistance?

a) The pair in parallel.

b) The pair in series.

c) The two combinations have the same resistance.