Question

If some electrons are added to a positively charged conducting cone, the surface charge density of the cone will:
1. Increase
2. Decrease
3. Remain unchanged
4. Can't say

Answer 1

Correct Answer - Option 2 : Decrease

CONCEPT:

Linear charge density:

• It is defined as the quantity of charge per unit length.
• Its SI unit is C/m.
• If ΔQ charge is contained in the line element Δl, the linear charge density λ will be,

​\(\Rightarrow \lambda=\frac{\Delta Q}{\Delta l}\)

Surface charge density:

• It is defined as the quantity of charge per unit area.
• Its SI unit is C/m2.
• If ΔQ charge is contained in the elemental area Δs, the surface charge density σ will be,

​\(\Rightarrow \sigma=\frac{\Delta Q}{\Delta s}\)

Volume charge density:

• It is defined as the quantity of charge per unit volume.
• Its SI unit is C/m3.
• If ΔQ charge is contained in the elemental volume Δv, the volume charge density ρ will be,

​\(\Rightarrow \rho=\frac{\Delta Q}{\Delta v}\)

EXPLANATION:

• Negative charge: A body having an excess of electrons.
• We know that when electrons are added to a positively charged body, the magnitude of the charge on the body decreases.
• Surface charge density is defined as the quantity of charge per unit area.

If ΔQ charge is contained in the elemental area Δs, the surface charge density σ will be,

​\(\Rightarrow \sigma=\frac{\Delta Q}{\Delta s}\)

• When some electrons are added to a positively charged conducting cone, the total charge on the cone will decrease so the surface charge density also decreases. Hence, option 2 is correct.

Electric Charge

• It is defined as the intrinsic property of certain fundamental particles like electrons, proton, etc, due to which they produce electric and magnetic effects.
• Types of electric charge
  1. ​Positive charge: A body having a deficiency of electrons.
  2. ​Negative charge: A body having an excess of electrons.
• Properties of electric charge
  • Like charges repel and unlike charges attract each other.
  • A charge is a scalar quantity.
  • If a system contains a number of point charges, then the total charge of the system is obtained simply by adding all the charges algebraically.
  • A charge is always quantized.
  • A charge will always remain conserved.
  • A charge is always associated with mass.
  • The unit of charge is the coulomb.