Basic Practice:
A) What is the Electric Potential 5 cm from a +4 nC charge? [ 7.2.102 V]
B) What is the Electric Potential midway between two -300 nC charges 4 m apart? [ -2.7 kV ]
C) If it takes 25 mJ of work to move a 500 nC charge from A to B what is the electric potential difference between A and B? [5.104 V]
D) If the electric potential difference between A and B is 2500 V how much energy is needed to move a 500 nC charge from A to B? [1.25 mJ]
Homework Problems:
1) An electron, initially at rest, is released and found to accelerate from point A to point B, where it is found to have 3.45.10-16 J of kinetic energy. What is the potential difference, ΔV, between A and B and which point is at higher potential?
2) The plot shows the electric potential along a line in space. What is the magnitude and direction of the E field along this line? A proton traveling in the +x direction is brought to a stop at x=3 mm. What was the kinetic energy of the proton at x=0?
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3) It takes 25.0.10-4 J to move a -7.50 µC charge from A to B. The charge was at rest at point A and had 4.83.10-4 J of kinetic energy when it reached point B. What is the electric potential difference, ΔV, between A and B?
4) In order to split a nucleus a proton must penetrate through the E field to reach the nucleus of a Si atom. There will be no E field to contend with until the proton begins to enter the fringes of the atom at a distance of 10 nm. The proton will reach the nucleus 3.6.10-15 m. from the center of the Si atom. What initial kinetic energy must a proton have to reach a Si nucleus (q=+14e) under these circumstances? Because an atom is a neutral object from a distance you should assume no E field until the proton gets 10 nm from the Si atom. From that point on consider only the field produced by the nucleus which is certainly an oversimplification but acceptable for this problem.
5) Consider two equal positive charges (q=+2.0 µC) a distance of 3.0 cm apart. What is the electric potential midway between the two charges? What is the E field at this point?
6) Consider two equal and opposite charges (q=±2.0 µC) a distance of 3.0 cm apart. What is the electric potential midway between the two charges? What is the E field at this point?
7) (calc) A line of charge extends from -L to the origin of the x axis. A charge Q is uniformly distributed along this line. Determine ΔV (what is this ΔV measured relative to?) along the positive x axis a distance “b” from the origin. (symbols, not numbers)
8) Pictured below is a line of charge with total charge Q which extends from -b to +b along the x axis. What is the electric potential at the point a distance a along the y axis? (no tricky approximations are needed here and the integral is in the back of your book!)
9) 3 charges are arranged along a line with -2q in the middle and +q a distance d on either side. This is called a quadrupole. Determine V a distance x from the central charge along the line of the charges. Make suitable approximations for the case where d is much less than x (d<<x). (hint: V proportional to 1/x3)
[kq{2d2)/x3}] /[2.0.105 V/m, 9.6.10-17 J] /[k(Q/b)ln{(b+(b2+a2)1/2)/a}]/[270 V, A is higher] /[9.0.10-13 J, 3.0.107 m/s]/[0 V, 1.6.108 N/C]/[k(Q/L)ln{(b+L)/b}]/[2.2 kV]/[2.4.106 V, 0 N/C]
