Question

1) You move a negative charge relative to a positive charge, such that the potential energy between the two decreases. Gravity should be ignored. This means you must be:

		a)Bringing them closer to one another
		b)Moving them apart
		c)Either or
		d)Cannot be determined

2) The amount of work needed to create a dipole of charge Q and distance a is:

		a) −kQ^2/a
		b) kQ2/a
		c) None of the above

Answer 1

1) The potential energy is given as below:

.............(1)

In equation (1) above, following should be noted:

[1] q is the magnitude of the charges.

[2] r is the relative distance between the charges, q.

[3] where is the permittivity of free space.

[4]   or U(r) is inversely proportional to the distance between the charges.

[5] Due to presence of negative q, U(r) is negative.

[6] As r increases, U(r) will tend to decrease upto a certain value where it will be minimum and then start increasing. After a certain increase, it will saturate for further increase in distance.

Answer: (b) Moving them apart.

2) A dipole is created when 2 charges (Q) of equal magnitude but opposite polarities (signs) are brought together such that they start behaving as a single system.

Potential energy of a system with charges q₁ and q₂ , distance "r" apart from each other is given by:

For a dipole, (magnitudes) BUT their charges will be opposite to each other. Hence, potential energy will be

where a is the distance between the charges "Q". For such a dipole the dipole moment will be given by  

which is the most fundamental characteristic of any dipole (only magnitude of the charges is considered, not sign).

ANswer : (a)