We will now try to find which of the four configurations (parallel, anti-paralle

Question

We will now try to find which of the four configurations (parallel, anti-parallel head-to-tail, and head-to-head) has the least potential energy. For the purpose of comparing the energies, we can omit the quantity Q_1Q_2/4 pi epsilon_0, which will be constant factor. Consequently we will work only with the term. For each configuration, compute the total potential energy (again, omit the Q_1Q_1/4 [I epsilon_0 term). Use cm for distance. The answers will be in a somewhat arbitrary unit, but this is OK for the purpose of comparing potential energies between configurations. Watch your signs Show your work. Connect charges with a line to show the pain of charges, write the value for that pair on the line and compute the total energy for each. Parallel: Total potential electrical energy Anti parallel Total potential electrical energy Lined up head to tail:

Explanation / Answer

17)

For the parallel configuration :

Potential energy = k*-Q*Q/d + k*(-Q)Q/sqrt(2)*d + k*Q*Q/d + k*(Q)*Q/d + k*(-Q)Q/sqrt(2)*d + k*(-Q)*Q/d

= k*Q^2/d*(-1 -1/sqrt(2) + 1 +1 -1/sqrt(2) - 1)

= (k*Q^2/d)*(-sqrt(2))

18)

For anti parallel combination :

Potential energy = k*-Q*Q/d + k*(-Q)(-Q)/sqrt(2)*d + k*Q*-Q/d + k*(-Q)*Q/d + k*(Q)(Q)/sqrt(2)*d + k*(Q)*(-Q)/d

= k*Q^2/d*(-1 +1/sqrt(2) - 1 -1 +1/sqrt(2) - 1)

= (k*Q^2/d)*(sqrt(2) - 4)

19)

For lined up head to tail :

Potential energy = k*(Q)(-Q)/d + k*(Q)(Q)/2d + k*(-Q)(Q)/d + k*(-Q)(Q)/3d + k*(-Q)(-Q)/2d + k*(-Q)*(Q)/d

= k*Q^2/d *(-1 +1/2 - 1 -1/3 +1/2 -1)

= k*Q^2/d *(-7/3)

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