16. Three point charges of values +1.0 C, +2.0 C. and +3.0 C are located at the

Question

16. Three point charges of values +1.0 C, +2.0 C. and +3.0 C are located at the corners of an equilateral triangle of sides 1.0 m. It is desired to find the work required to move these charges inward to the corners of an equilateral triangle of smaller side 0.50 m, centered the same as the larger triangle (see diagram). a). Calculate the potential energy of the three charges at the corners of the larger triangle. b). Imagine the charges having moved in to the corners of the smaller triangle and calculate the potential energy of this new configuration. e). How much work was required by some external agent to move these three charges inward to the smaller triangle?

Explanation / Answer

We know that, electric potential energy is

Hence we have to calcualte the potential energy at the corners of the larger triangle

So first we calculate at potential energy at corner A
= (K QAQB / R) +(KQAQC/R) = 5 K where R is the side of larger triangle, K is constant= 9*109
Similarly we will calculate at B
= (K QBQC / R) +(KQBQA/R) = 8K
Similarly at corner C
= (K QCQB / R) +(KQCQB/R) =9K

when we shift it to the lower triangle corners then the potential energy at each corner of the lower triangle becomes
At corner a
= (K QAQB / r) +(KQAQC/r) = 10K where r is the side of the lower triangle.
At corner b
= (K QBQC / r) +(KQBQA/r) = 16K
At corner c
= (K QCQB / r) +(KQCQB/r) = 18K

(3) To calcualte the workdone in moveing the charge simply we will substract the potential energy at corner A and a , B and b , C and c.

Work done in moving charge A = 5K
Charge B = 8K
Charge C = 9K
on putting the value of K we will find the values

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