Question

If a body contains x number of electron and y number of protons, then the magnitude of charge on the body will be:
1. (x - y) × 1.6 × 10^-19 C
2. (x + y) × 1.6 × 10-19 C
3. (y - x) × 1.6 × 10-19 C
4. -(y + x) × 1.6 × 10-19 C

Answer 1

Correct Answer - Option 3 : (y - x) × 1.6 × 10-19 C

CONCEPT:

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.

⇒ 1 coulomb = charge on 625 × 1016 electrons

EXPLANATION:

Given x = number of electrons, and y = number of protons

Quantisation of charge:

• Experimentally it is established that all free charges are integral multiples of a basic unit of charge denoted by e.
• This basic unit of charge is the charge that an electron or proton carries.
• Thus charge q on a body is always given by:

⇒ q = ne

Where n = integer and e = 1.6 × 10^-19 C (Charge on one electron or one proton)

So the charge on the body due to x number of electrons,

⇒ q_e = -x × (1.6 × 10-19 C)

And the charge on the body due to y number of protons,

⇒ qp = y × (1.6 × 10-19 C)

• 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.
• So the total charge on a body is given as,

⇒ q = q_e + q_p

⇒ q = (y - x) × 1.6 × 10^-19 C

• Hence, option 3 is correct.