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Physics 3:  Introduction to Electricity & Magnetism 

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Javier Montenegro Joo

jmj@VirtualDynamics.Org

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(1) Two point charges Q1  and Q2   are placed on a line at  45o   with the horizontal x-axis and separated a distance L.   A third charge   Q  is placed on the line passing by  Q1  and Q2 , and at a distance b of Q.  Determine the relationship between Qand Q2    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 Q1   and Qmust 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 Qo are placed equidistantly on a semi-circumference 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 semi-circle (see the sketch below) have been numbered 1,2,,5.  Since the charges on the edge of the semi-circle 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 F3 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 45o  with the x-axis, both have vertical and horizontal components, but it is evident that their vertical components cancel each other, remaining only their horizontal components along the x-axis.

 
(4) Consider a right triangle whose equal sides have a length b and, which has a charge Q in its right angle. Charges Qo and Qo  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:

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