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 3. In cases A and B shown at right there are two positive point charges +0 each a distance s away from a third positive point charge +g a. +0 tg tq 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. +0 4 *O Case B Case A In case C, two positive point charges +20 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 shown is the same in both cases.) b. +q Case C Case D 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

3. a. as the Net electric force on charge +q depends on cos(theta/2), where theta is the angle between the two vectors joining the two +Q charges with +q charge

and lower the value of theta, higher is its cos value

hence, Force in case of Case B is greater than force in case of case A

b. In case C, the y component of forces cancel each other out, from symmetry

so Net force on +q = 4kqQ(sin(alpha))/s^2

In case D, due to symmetry again the y component of forces cancel out

so Net force on +q = 2kQsin(alpha)/s^2 + 2kQ*sin(alpha + (90 - alpha)/2)/s^2 = 2kQsin(alpha)/s^2 + 2kQ*sin((90 + alpha)/2)/s^2

now, (90 + alpha)/2 > alpha when

90 > alpha [ always ]

hence Force in case D is more than the force in case C

c. Force on +q incase E -> kqQ/s^2

Force on +q in case F -> 2kqQ[cos(alpha)/10 + cos(2*alpha)/10 + cos(3*alpha)/10 + cos(4*alpha)/10 + cos(5*alpha)/10]/s^2

cos(alpha) + cos(2*alpha)+ cos(3*alpha) + cos(4*alpha) + cos(5*alpha) < 5 for alpha being some +ve small angle

so Force on +q in case F is less than force on +q in case E

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