Question

Explain potential energy of a system of charges. Calculate energy needed to place charge q at each corner of a square of side l

Answer 1

Answer:

3. REASONING AND SOLUTION The potential at a point in space that is a distance r from a point charge q is given by Equation 19.6: . When more than one point charge is present, the total potential at any location is the algebraic sum of the individual potentials created by each charge at that location.

Three point charges have identical magnitudes, but two of the charges are positive and one is negative. These charges are fixed to the corners of a square, one to a corner, as shown in the figure.

The potential at the empty corner is given by

Using q to denote the magnitude of each charge, we have the following possibilities:

 

q1 and q2 are positive:  

q1 and q3 are positive:  

q2 and q3 are positive:  

 

In each case, the potential at the empty corner is positive.

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Answer 2

Potential energy of a system is defined as the ratio of potential difference and the charge on the system.

Explanation:

          Potential energy = $\frac{potential \\ difference}{chrge}$

                                      = $\frac{V}{q}$

Here, V is the potential difference and the q is the charge on the system.

Basically, it is the work done by the system to transfer the charge through a certain distance by the potential difference.

Energy needed = $\frac{q^{2}}{l^{2} \times 4\pi e }$

l is the side given and  e is the permittivity.