Forces on Five Fqual Charges Five equal positive charges with value q are arrang

Question

Forces on Five Fqual Charges Five equal positive charges with value q are arranged in the shape of a cross, as shown in the figure. The distance from one charge to another is a. Starting at the top and working clockwise, the charges are numbered 1 - 5. Determine the direction of F_1, the total force on charge 1. Determine the magnitude of F_1, the total force on charge 1. Then write down F_1 using unit-vector notation. Write down the forces on the remaining charges ( F_2, F_3, F_4, and F_5 ), using unit-vector notation. Note: It is not necessary to calculate anything in order to answer part (c).

Explanation / Answer

(a) The forces from charges 2 and 4 cancel each other out. The resulsive forces from charge 3 and 5 add up upwards. So the direction of force F1 on charge 1 is directly upwards.

(b) F1 = (Force due to charge 3) + (Force due to charge 5)

F1 = (kqq/a2) j^ + (kqq/(2a)2) j^

F1 = (5/4) kq2/a2 j^

(c) The magnitude for forces F2, F3 and F4 will be same as that of F1, but direction will differ.

F2 = (5/4) kq2/a2 i^

F3 = - (5/4) kq2/a2 j^

F4 = - (5/4) kq2/a2 i^

The nest force on charge 5 will be zero as repulsive forces from all the four charges will cancel each other out. Thus

F5 = 0

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