Phy 214 Test 1 8 pts each Feb. 2, 2007

(4 pts Absolutely FREE!)

1. In each diagram below, draw a vector showing each force vector and the net force on the round particle due to all the square fixed charges. Make sure all vectors are drawn to lengths indicating relative magnitudes of forces.

2. A large positive charge pulls on a distant electron. How does the net force on the electron change when a slab of glass is placed between the large positive charge and the electron ? Explain using ONLY carefully labeled diagrams. (Be sure to show ALL the forces on the electron before determining the net force on the electron.)

3. a. In the diagram, a rubber rod is given a charge Q distributed uniformly over it by rubbing it with fur. It is noticed that when an uncharged metal ball is suspended by a string at a particular location near the end of the rod is drawn toward the rod by some mysterious force. Show the distribution of charges on both the rod and the ball and explain why this occurs.

3 b. When the rubber rod is removed, and replaced by a metal rod of the same length which has been given the same amount of charge, it is found to cause the ball to come much closer. Show the distribution of charges on both the rod and the ball and explain why this occurs.

4. These two solid spheres initially have the charge evenly distributed on their surfaces. Find magnitude and direction of the electric field at the points A, B, and C .

5. Many people believe current output by a battery is fixed.

a. Describe (or draw ) two different circuits in which the same battery produces two different amounts of current.

b. Explain how you know the current is different in the two circuits.

6. A single wire across the top of the compass causes a deflection of 30° in needle. If it is now curved back along side the first wire, the needle will now have what deflection?

7. The charges in the diagram below are located on the corners of a square that is 6 m on each side. Find the magnitude and direction of the electric field at P. (Hint # 1: There is a really hard way to do this problem and there is a really really easy way to do it. ) (Hint # 2: Well now, tests are supposed to be learning experiences. This problem is a test to see whether or not you learned anything from the experience of doing problem 1.)

8. What you see in the figure below is a cut-away view of a hollow metal sphere. The gray area indicates solid metal. The white region in the center indicates the hollow center, at the center of which has been placed, some magical how, an unknown charge Q3. We have been able to detect a 20 C charge Q₂ on the inside surface of the shell, and also that the electric field is 1.8 x 10⁹ N/C at a distance of 5 m from the center of the system, we need your assistance to determine what charge Q₃ is located at the center, and how much charge Q₁ is on the outer surface of the sphere.

Thank you for your help, we have every confidence that you can solve this problem and save our mission!

9. Where would you place an electron ( charge is 1.6x10^-19C.) so that the electric field at P would be 300N/C to the left.

10. Consider a thin plastic rod. The rod carries a uniformly distributed positive charge Q. Follow the steps below to obtain the components E_x and E_y of the electric field at the origin, due to the rod.

a) Use a diagram to explain how you plan to cut up the charged rod, and draw the DE contributed by a representative piece.

b) Express algebraically the contribution each piece makes to the x and y components of the electric field . Be sure to show your incremental component dE of the electric field on your drawing. (Recall that the arc length Ds of a circular arc of radius R , subtended by an angle of Du, is R Du.)

c) Write the summation as an integral for each component of E, and simplify the integral as much as possible. State explicitly what the range of your integration variable is.

d) 5 points Bonus! Evaluate the integrals to find E_x and E_y.

11. Here is a view from above of a portion of a circuit containing three identical light bulbs (the rest of the circuit including the batteries is not shown).

(a) The compass is placed on top of the wire, and it deflects 20 degrees away from north as shown (the wire is underneath the compass). What direction are the electrons moving at location Pl ? How do you know?

b) In the steady state, 3 x 10⁸ electrons pass location Pl every second. How many electrons pass location P2 every second? Explain briefly.

(e) Describe the relative brightness of bulbs Bl, B2, and B3. Explain briefly.

12. a. Connect the circuit below.

b. then measure and record the deflection angle in each of the boxes.

c. circle the correct response.

a. These two bulbs have the same brightness

b. The long bulb is brighter than the round bulb.

c. These two bulbs have the same current flowing through them.

d. The electric fields in the two bulb filiments are the same.

5 Pts Bonus each!

B1. If current flow is inversely proportional to length of wire, (you can think of two bulbs as one bulb with twice the length), why doesn't the current drop in half when a second identical bulb is placed in series ?

B2. On a clear and carefully drawn diagram, place a zorac nucleus and an electron in such a way that the electric field due to these charges is zero at a location marked x. (A zorac nucleus contains three protons and three neutrons.) Explain briefly but carefully, and use diagrams to help in the explanation. Be quantitative about the relative distances (That means give a formula for one distance in terms of the other, or give an algebraic expression for the ratio of the two).