Each of the following parts involves a comparison of the net electric force exer

Question

Each of the following parts involves a comparison of the net electric force exerted on a positive charge + q in two different cases. In cases A and B shown at right there are two positive point charges +Q each a distance s away from a third positive point charge +q. Is the net electric force on the +q charge in case A greater than, less than, or equal to the net electric force on the +q charge in case B? Explain. In case C, two positive point charges +2Q are each a distance s away from a third positive point charge +q. In case D, four positive point charges +Q are each a distance s away from a fifth positive point charge +q. (The angle a show is the same in both cases.) Is the net electric force on the +q charge in case C greater than, less than, or equal to the net electric force on the +q charge in case D? Explain.

Explanation / Answer

3a) The net electric force on +q charge in case of A is equal to the net electric force on +q charge in case B

since from the principle of super position

in case A net force Fa = kqQ/s2 + kqQ/s2

     = 2kqQ/s2

  incase B net force is also Fb = kqQ/s2 + kqQ/s2  = 2kqQ/s2

     i.e Fa = Fb

B) Fc =   kq(2Q)/s2 +  kq(2Q)/s2 = 4kqQ/s2

Fd =   kqQ/s2 +   kqQ/s2 +  kqQ/s2 +  kqQ/s2

=  4kqQ/s2

hence Fc = Fd

When a number of charges are present, the total force on a given charge is equal to the vector sum of forces due to the remaining other charges on the given charge.

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