### Electric Potential Problems with Solutions

Electric potential is a physical quantity that explains the flow of current from one place to other. It is treated like a  scalar quantity and it is measured with a unit called volt. It is the amount of the work done in getting a unit positive charge from infinite to a particular place.

When multiple charges are separated by a certain distance, we can find the effective potential at a given point due to all of them. We need not bother about the direction of it as it is a scalar quantity.

We cannot get a neutral point in terms of voltage between two as they actually add up at the point. We can  get a neutral point of potential between dissimilar charges. Simply because potential due to a positive charge is positive and potential due to a negative charge is negative. At a common point if both of them cancel and hence we can get a neutral point.

Problem and solution

Let us consider a problem here in line with the above issue. Let us consider two charges one positive and other negative with magnitude 10 coulomb and 15 coulomb separated by 40 centimeter on the X- axis. We need to know the neutral point which experience a zero potential.

Here there are three possibilities. The first possibility is to find it from the first charge. It is as shown in here below.

In case two, would like to find a neutral point not in between them but beyond them. that is also possible and it is as shown in the diagram below.

One more possibility is to find a neutral point outside them on the same axis but from the other end that is from the second charge. It is as shown in the diagram below.

Problem and solution

In another problem, we would like to measure the work done in moving a charge between two points which are at two different potential. We need to use simple potential definition and potential energy difference concept to solve this problem. It is as shown below.

Problem and Solution

Let us consider infinite charges are placed on x axis at regular separation and we need to measure the potential due to all of them at the origin. There will be potential due to all of them and we need to all the potentials at that point to get the total potential. Be clear that we need not worry about the direction as it is a scalar quantity. This is how potential is different from electric intensity. Here is the problem and solution below for your observation.

Problem and Solution

Let us consider four identical charges placed at the four corners of a square and we would like to measure the effective potential at the cross section of the diagonals.

we need to measure the distance between the charge and cross section of the diagonals that can be done easily using Pythagoras theorem.

All potentials are positive as they all are due to positive charges and hence they have to be added to get the total value at the cross section. It is done as shown in the diagram below.

Problem and Solution

Just like the above problem, now we would like to measure the potential at the centroid of a equilateral triangle and the way of solving the problem is similar.

The solutions is as given below.

Problem and Solution

This problem is about number of liquid drops combined together and getting into a big drop. We use the definition of potential as well as conservation of volume as shown below.

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