Question

a. Two charges are placed on the x axis 5 m apart with the left charge on the origin. The left charge has a charge of 4uC and the right has a charge of -8uC. A 24C must be placed somewhere other than infinity), so that it experience no net force. Fully explain approximately where you expect this point to be. You must supply reasoning for choosing the approximate location of the point to receive full credit. b. Mathematically find the location of the point in part a

Answer 1

a.

4Uc - - - - - - - ХиС - - - - - - - - SM auc А 1, 2 и 3 • 2 и с Зо

The diagram show the three posibilities to locate the third charge (positions A, B or C). At position A, electric force between charges 1 and 3 is repulsive, then it goes to the left, while force between charges 2 and 3 is atractive, so it goes to the right. A similar behavior is observed at position C. Only in position B net electric force is not 0. Then, only at position A or C it could be possible to get a net electric force equal to 0.

b.

To find the place to put the third charge, we have to consider static equilibrium. Then:

F = 7 → |F13) = |F23

K 1993] = k19293 r 13 r23

191. r 3 = 1920-1

Defining x as the distance from charge of 4 micro Coulombs (q1) to the third charge, then, for option A:

4(x + 5)2 = 8(2)2 + 2? – 10x – 25 = 0+1=5(1 V2)

Since x is defined as a magnitude, then should be positive. Then:

1 = 5 (1 +V2) – 12.071m

And, for option C:

4(x – 5)2 = 8(x)2 + 2? + 10x – 25 = 0 + 1 = 5(-15V2)

Again, x is defined as a magnitude, then:

1 = 5(-1 +V2) — 2.071m

This result is lesser than 5, then it is not possible to locate the third charge in position C (where x should be greather than 5m).

Conclusion. The only one position where net electric force is 0 for the third charge is at 12.071m to the left of charge of 4 micro Coulombs (position A).