Question

The force between two charges 5μC and 6μC placed at a certain distance from each other is F. If one more charge of magnitude 2μC is placed near the charge 5μC then the force between the charge 5μC and 6μC will be:
1. F
2. More than F
3. Less than F
4. Can't say

Answer 1

Correct Answer - Option 1 : F

CONCEPT:

The force between multiple charges:

• Experimentally, it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. 
• The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition.
• The principle of superposition says that in a system of charges q₁, q2, q3,..., q_n, the force on q₁ due to q₂ is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges  q2, q3,..., qn. The total force F₁ on the charge q₁, due to all other charges, is then given by the vector sum of the forces F₁₂, F13, ..., F_1n.

\(\Rightarrow \vec{F_1}=\vec{F_{12}}+\vec{F_{13}}+...+\vec{F_{1n}}\)

EXPLANATION:

• Experimentally, it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. 
• The individual forces are unaffected due to the presence of other charges.
• Therefore if the force between the two charges 5μC and 6μC placed at a certain distance will not be affected by the presence of any other charge.
• So the force between the two charges 5μC and 6μC placed at a certain distance will remain F when one more charge of magnitude 2μC is placed near the charge 5μC. Hence, option 1 is correct.