Force on charge in an electric field. Two stationary point charges, each equal i

Question

Force on charge in an electric field. Two stationary point charges, each equal in magnitude to q [C], are located a distance d [m] apart. A third point charge is placed somewhere on the line separating the two charges and is allowed to move. The charge is free to move in any direction: (a.) If the stationary charges are positive and the moving charge is positive, it will move to the midpoint between the two stationary charges. Is this a stable position? If not, where will the charge eventually end up if its position is disturbed? (b.) What is the answer to (a.) if the stationary charges are positive but the moving charge is negative? (c.) What is the answer to (a.) and (b.) if the stationary charges are negative.

3.14 Force on charge in an electric field. Two stationary point charges, each equal in magnitude to q IC], are located a distance d Im] apart. A third point charge is placed somewhere on the line separating the two charges and is allowed to move. The charge is free to move in any direction: (a) If the stationary charges are positive and the moving charge is positive, it will move to the midpoint between the two stationary charges. Is this a stable position? If not, where will the charge eventually end up if its position is disturbed'? (b) What is the answer to (a) if the stationary charges are positive but the moving charge is negative? (c) What is the answer to (a) and (b) if the stationary charges are negative?

Explanation / Answer

Answer:-a) At the mid point the force on moving charge is same in magnitude but opposite in direction so it is a case of dynamic equilibrium. Any disturbance will make the moving charge to leave the position on the line joining of two stationary charges and moving charge will take position either above or below the line.

b) If moving charge is negative and stationay charges are positive then at the middle of line the moving charge will be at stable condition. If a disturbance is made then moving charge will move towards that stationary charge which is near to moving charge.

c) When stationary charges are negative and moving charge is positive the result is same as part b.i.e moving charge will be stable at mid point and any disturbance will make moving charge to attach with nearest stationary charge.

when stationary charges are negative and moving charge is also negative then case is same as part a i.e dynamically stable at mid point and any disturbance will cause the charge to leave the line and take position either above or below . The charhe will move till net force on that is zero ideally that will happen at infinite distance from line but practically after some distance the appreciable force on moving charge will be zero.

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