Question

In the absence of other conductors, the surface charge density
A. Is proportional to the charge on the conductor and its surface area
B. Inversely proportional to the charge and directly proportional to the surface area
C. Directly proportional to the charge and inversely proportional to the surface area
D. Inversely proportional to the charge and the surface area

Answer 1

In order to find the correct option, first recall the formula for surface charge density. Then observe how the surface charge density is dependent on charge on the conductor and its surface area. And carefully check which of the following options matches with the formula of surface charge density.

Complete answer:
Surface charge density can be defined as the measure of accumulation of electric charge per unit area of the conductor. As no other conductors are there, so surface charge density can be written as,
$\sigma = \dfrac{Q}{A}$
$Q$ denotes the charge of the conductor and $A$ denotes the surface area of the conductor.

Now, we compare the given options with the formula of surface charge density.
Option A: In this option it is given that surface charge density is proportional to the charge on the conductor and its surface area but from the formula of surface charge density we observe that surface charge density is inversely proportional to its surface area.

Option B: In this option it is given that surface charge density is inversely proportional to the charge and directly proportional to the surface area. Both of these conditions are incorrect as we observe from the formula that charge is directly proportional to surface charge density and surface area is inversely proportional to surface charge density.

Option C: In this option it is given that surface charge density is directly proportional to the charge and inversely proportional to the surface area. And this is correct as we observe from the formula that charge is directly proportional to surface charge density and surface area is inversely proportional to surface charge density.

Option D: In this option it is given that surface charge density is inversely proportional to the charge and the surface area. The first condition is incorrect as we observe from the formula that charge is directly proportional to surface charge density.

Hence,option C is the correct answer.

Note: There are three kinds of charge density. First is line charge density, which is the measure of electric charge distribution per unit length of the conductor. Second is surface charge density, which we have discussed in the above question. And third is volume charge density, which is the measure of electric charge distribution per unit volume of the conductor.