## Sunday, July 17, 2016

### Resultant Force and Coloumb's Law of Electric Force Problems and Solutions

Electric charges apply force of repulsion on similar type of charges and apply force of attraction on opposite kind of charges. The magnitude of the force of attraction or repulsion  can be measured using Coloumb's Law of force.

If there are multiple force acting on a charge due to multiple charges, we need to use vector laws of addition to identify the resultant of all the forces. We can use parallogram law and triangle law of vectors to find the resultant of the total force acting on the system.

If three identical charges are at three corners of the triangle, the resultant force on a charge at the centroid of the triangle is zero as three force acting on it behaves like three force of triangle law and hence their resultant force is zero.

It can be further shown that if one charge at any corner is different in nature, resultant at the center is not going to be zero as the forces are not going to cancel out. We can find the resultant as shown below.

The case is same when four identical charges are placed at the four corners of the square. The resultant force on the fifth charge placed at the cross section of the diagonals is zero. If the charges change their nature, the effective force will be different.

Resultant force due to multiple charges

Let us consider two similar charges at the two corners of equilateral triangle and we would like to measure the resultant force at the third corner of the triangle. The two forces acting on the third charge are equal in magnitude but having some angle between them. To find the resultant force, we need to use parallogram law of vectors.

We can repeat the same and solve the problem, when the charges are in opposite nature but the resultant is different from the earlier case. The reason is though the forces are same like the previous case, they do act in opposite directions and hence the resultant force is different.

Let us assume a scenario where four identical charges are placed at the four corners of the square and we need to measure the resultant force on any charge that is at the any corner of the square. On the forth charge, there are three force acting due to three charges. Forces due to two charges are equal in magnitude and they are perpendicular to each other. Their resultant is along the direction of the third force due to the third charge. We need to use parallogram law to find the total force acting on it. It is as solved below.

We can also find the magnitude of the charge that has to placed at the cross section of the diagonals, so that the entire system is in equilibrium.

We can solve a problem where good number of charges are placed on the x axis from a initial point and we need to measure what kind of charge that has to be placed at the origin so that the resultant force on it will be zero.

Let us consider identical charges places on horizontal axis as shown and the resultant force can be measured as shown below.

If we put different charges in contact, there will be flow of charge from one to other until equilibrium is reached. As charges are redistributed, the force between them will change once they are separated back to some distance of separation.

Problem and Solution

Let us consider two charges of different nature separated by a certain distance of separation.Now this two charges are got into contact and separated back  to a different distance. What is the new force between them ?

Solution

When two different charges are brought into contact, there will be flow of charge from one body to other until they get equilibrium. With the new charge distribution and with different distance of separation, new force between them can be measured once again using Coloumb's law of force as shown.

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