practice

1. A charge of -1.0 μC is located on the y-axis 1.0 m from the origin at the coordinates (0,1) while a second charge of +1.0 μC is located on the x-axis 1.0 m from the origin at the coordinates (1,0). Determine the value of the following quantities at the origin …
   1. the magnitude of the electric field,
   2. the direction of the electric field,
   3. the electric potential (assuming the potential is zero at infinite distance), and
   4. the energy needed to bring a +1.0 μC charge to this position from infinitely far away.
2. A proton (mass m, charge +e) and an alpha particle (mass 4m, charge +2e) approach one another with the same initial speed v from an initially large distance. How close will these two particles get to one another before turning around?
3. sketch-v.pdf
   The diagram on the accompanying pdf file shows the location and charge of four identical small spheres. Find the electric potential at the five points indicated with open circles. Use these results and symmetry to find the potential at as many points as possible without additional calculation. Write your results on or near the points. Sketch at least 4 equipotential lines. Pick round values seperated by a uniform interval. At least one of the lines should be disconnected.
4. Write something completely different.

conceptual

1. In a region where the electric field is constant, as it is between two oppositely charged parallel plates, is the voltage also constant? Explain your answer.
2. In a region where the electrical field is zero, as it is inside a charged conducting sphere, is the voltage also zero? Explain your answer.
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4. Two related questions.
   1. What do the electric fields lines look like in a region where the electric field is uniform?
   2. What do they look like in a region where the electric potential is uniform?

numerical

1. The inside of a human nerve cell is more negative than the outside by about −80 mV. When a nerve impulse propagates down an axon, the polarity reverses and the inside is more positive than the outside by +40 mV. This action potential lasts only a millisecond and then the original resting potential is restored. All of this takes place in the space of about 4 nm, the thickness of the cell membrane.
   1. What is the magnitude and direction of the electric field across the membrane of a neuron during …
      1. the resting phase
      2. the action phase
   2. How much work is done moving a single sodium ion (Na⁺) across the cell membrane of a neuron? State your answer in …
      1. joules
      2. electron volts
   3. What is the power of this microscopic event?