11. For the equipotential contour map shown below: a. Estimate the electric field magnitudes Ęα and Ę at points a and b. Show how you made your estimate. b. On the contour map, draw the electric field vectors at points a and b. OV a 10 V 20 V 30 V 40 V X 4 m 3 m 2 m ] m 0 m

(a) Use the exact result from Example 24.4 to find the electric potential created by the dipole described in the example at the point (3a, 0). (b) Explain how this answer compares with the result of the approximate expression that is valid when x is much greater than a.

A spherical balloon contains a positively charged object at its center. (i) As the balloon is inflated to a greater volume while the charged object remains at the center, does the electric potential at the surface of the balloon (a) increase, (b) decrease, or (c) remain the same? (ii) Does the electric flux through the surface of the balloon (a) increase, (b) decrease, or (c) remain the same?

The electric field strength between two parallel conducting plates separated by 4.00 cm is 7.50 104 V/m. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?

An amoeba has 1.001016protons and a net charge of 0.300 pC. (a) How many fewer electrons are there than protons? (b) If you paired them up, what fraction of the protons would have no electrons?

A balloon clings to a wall after it is negatively charged by rubbing. (a) Does that occur because the wall is positively charged? (b) Why does the balloon eventually fall?

A thin conducing plate 2.0 m on a side is given a total charge of 10.0C . (a) What is the electric field 1.0 cm above the plate? (b) What is the force on an electron at this point? (c) Repeat these calculations for a point 2.0 cm above the plate. (d) When the electron moves from 1.0 to 2.0 cm above the plate, how much work is done on it by the electric field?

(a) A certain parallel-plate capacitor has plates of area 4.00 m2 , separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

Oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600. V exists between the plates. (a) What is the magnitude of the electric field between the plates? (b) What is the magnitude of the force on an electron between the plates? (c) How much work must be done on the electron to move it to the negative plate if it is initially positioned 2.90 mm from the positive plate?

Figure P24.23 shows several equipotential lines, each labeled by its potential in volts. The distance between the lines of the square grid represents 1.00 cm. (a) Is the magnitude of the field larger at A or at B? Explain how you can tell. (b) Explain what you can determine about E at B. (c) Represent what the electric field looks like by drawing at least eight field lines. Figure P24.23