VirtualDynamics UniversitySolved UniversityPhysics ProblemsPhysics 3: Introduction to Electricity & Magnetism <<< Coulomb's Law >>>Javier Montenegro Joo jmj@VirtualDynamics.Org 

<<< Coulomb's Law >>> 
(1) Two point charges Q_{1} and Q_{2} are placed on a line at 45^{o } with the horizontal xaxis and separated a distance L. A third charge Q_{o } is placed on the line passing by Q_{1} and Q_{2} , and at a distance b of Q_{1 }. Determine the relationship between Q_{1 }and Q_{2 }so that these two charges do not experience any force. Solution. The 45° orientation of the line where the electric charges are placed is irrelevant. Since Q_{1 } and Q_{2 }must not experience any force:_{ } 
(2) Two equal small cork balls of mass m, are hanging from the same point by insignificant weight threads of length L. The balls are loaded each with a charge Qo, so that both separate a distance d due to mutual repulsion. Determine the charge Qo in each ball. Solution.

(3) Five point electric charges of equal magnitude Q_{o} are placed equidistantly on a semicircumference of radius R, which is centered at the origin of coordinates. Determine the total force on a charge of magnitude Q placed at the origin of coordinates. Solution. For didactic reasons the charges on the edge of the semicircle (see the sketch below) have been numbered 1,2,…,5. Since the charges on the edge of the semicircle are all equal, and all of them are at the same distance to the center, then all of them exert the same strength on charge Q. It is obvious in the sketch that the third charge exerts a horizontal force F_{3} on charge Q at the center. It can be seen that the force between charges 1 and Q points downwards, while the force between charges 5 and Q, points upwards, therefore these two forces cancel each other. The forces exerted by charges 2 and 4 on charge Q at the center, point both at 45^{o } with the xaxis, both have vertical and horizontal components, but it is evident that their vertical components cancel each other, remaining only their horizontal components along the xaxis.

(4)
Consider a right triangle whose equal sides have a length b and, which
has a charge Q in its right angle. Charges Q_{o} and –Q_{o}
have been placed respectively, in the two other vertexes of the
triangle. Determine the total electric force on charge Q. Solution. The sketch below shows the positive charge Q in the right angle of the right triangle and the charges –Qo and +Qo at its vertexes named 1 and 2, respectively. It can be seen the attractive force F1 and the repulsive force F2 that charges Qo and Qo exert on Q, respectively. As both charges have the same magnitude, their vertical components F1y and F2y cancel each other. It can be seen that both charges, –Qo and +Qo generate a resulting force F1x + F2x in the –X direction. Under these conditions:
