Question

The force of attraction between two identical charges is 60 N. If the amount of charge is increased to twice of its initial, what will be the force now?

Answer 1

Answer:

• The Force between the charge's will be 240 N

Explanation:

Given, Initial Force of att. = 60 N.

Let the two charges be q₁ and q₂ respectively.

So, Now from the coulombs law we know that,

$\longrightarrow\sf F=\dfrac{1}{4 \pi \epsilon_{0}}\;.\; \dfrac{q_{1}q_{2}}{r^{2}}$

So,

$\longrightarrow\sf F \propto q_{1}\;.\; q_{2}$

As now in the second case both the charge is doubled to the initial value, lets find the force of attraction in the second case,

$\longrightarrow\sf \dfrac{F_{1}}{F_{2}} = \dfrac{q_{1}\;.\; q_{2}}{q_{3}\;.\; q_{4}}\\\\\\\\\longrightarrow\sf \dfrac{60}{F_{2}}=\dfrac{q_{1}\;.\; q_{2}}{2\;q_{1}\;.\; 2\; q_{2}}\\\\\\\\\longrightarrow\sf \dfrac{60}{F_{2}}=\dfrac{q_{1}\;.\; q_{2}}{4\;(q_{1}\;.\;q_{2})}\\\\\\\\\longrightarrow\sf \dfrac{60}{F_{2}}=\dfrac{1}{4}\\\\\\\\\longrightarrow\sf F_{2} = 60\times 4\\\\\\\\\longrightarrow\sf F_{2}=240 N$

∴ The Force between the charge's is 240 N.

Answer 2

Answer:

• If the amount of charge is increased to twice of its initial then force will be 240 N.

Explanation:

Given information,

The force of attraction between two identical charges is 60 N. If the amount of charge is increased to twice of its initial, what will be the force now?

• Initial force of attraction (F) = 60 N
• Amount of charge is increased to twice of its initial
• Now, force (F') = ?

By coulomb's law of electrostatic of identical point charges we know that,

➻ F = Kq²/r²

• Keep ‘K’ and ‘r’ constant

➻ F/q² = constant

➻ F/q² = F'/q'²

As we know that, the amount of charge is increased to twice of its initial.

• So, q' = 2q

➻ 60/q² = F'/(2q)²

➻ 60/q² = F'/(2q × 2q)

➻ 60/q² = F'/(2 × q × 2 × q)

➻ 60/q² = F'/(2 × 2 × q × q)

➻ 60/q² = F'/(4 × q²)

➻ 60/q² = F'/(4q²)

➻ 60/q² = F'/4q²

➻ F'/4q² = 60/q²

➻ F' = 60/q² × 4q²

➻ F' = 60/q² × 4 × q²

• In RHS ‘q²’ will be cancelled with ‘q²’

➻ F' = 60/1 × 4 × 1

➻ F' = 60 × 4

➻ F' = 240 N

• Hence, if the amount of charge is increased to twice of its initial then force will be 240 N.

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