Two point charges Q1 = +4.90 nC and Q2 = ?3.20 nC are separated by 45.0 cm. (a)

Question

Two point charges Q1 = +4.90 nC and Q2 = ?3.20 nC are separated by 45.0 cm. (a) What is the electric potential at a point midway between the charges? V (b) What is the potential energy of the pair of charges? J What is the significance of the algebraic sign of your answer? Positive work must be done to separate the charges. Negative work must be done to separate the charges.

Explanation / Answer

To calculate electric potential energy, use Coulomb's Law, Gauss' Law or Maxwell's first equation (They're pretty much just different ways of saying the same thing) and convert it to potential rather than force or electric field. I assume you've seen Coulomb's law? When converted to potential energy, it looks like: V = kQq/r (I use 'V' for potential energy, Q and q are the charges, r the distance between them and k an electrostatic constant: k = 1 / (4*pi*epsilon-0), where epsilon-0 is the permittivity of free space) Plug in the numbers: V = [ 1 / (4*pi*8.85E-12) ] * 5E-9 * -3E-9 / 0.35 = -4.766..E-27J I use E for standard form: 4E7 is 4x10^7. Potential energy for electricity is derived by assuming you bring a positive test charge from infinitely far away. At infinity, the potential energy is zero. If it is an attractive force (eg between opposite charges) then it is negative as you bring the two things closer together because they lose potential energy. You're attracted b) doing the above and dividing by half won't work because you have uneven charges and above you work out a potential (in Joules), whereas now you want ELECTRICAL potential (in Joules/Coulomb, or Volts). For this part you need to work out the electric potential of bringing a test charge from infinity to each charge in turn, and then the change in energy as it moves r/2 away from that object. Then add the two potentials together, keeping track of sign. Electrical potential energy equation is kQ/r (notice one fewer q, you now have a voltage) c) The answer above tells you the voltage, ie energy/charge. At 'very far away', you assume the limit r tends to infinity. ie its potential energy->0. (kQq/r as r gets very big ->0) Simply multiply the voltage worked out in b) by the 2nC to convert from energy/charge to just energy. You're moving it from a voltage of zero to the voltage you worked out above - that tells you the change in potential energy. Remember to change the sign when you convert from potential to work done so that the total change in energy = 0 and energy is conserved. You should end up with a positive work done; which makes sense. The total charge of the two objects is positive, so you would have to 'push' a positive charge to get it closer.

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