Question

Two equal charges placed 3m apart repel each other with force 0.1gf. Calculate the

magnitude of either charge​

Answer 1

Answer:

• The Magnitude of the charges (q) is 9.9 × 10⁻⁷ C

Given:

1. Electrostatic force of attraction (F) = 0.1 g F
2. Distance of separation (r) = 3 m.
3. Let the two charges have a magnitude equal to q

Explanation:

$\rule{300}{1.5}$

First we need to convert Force into S.I units.

We Know,

⇒ 1 g F = 0.0098 N

⇒ 1 g F = 9.8 × 10⁻³ N

Now,

⇒ 0.1 g F = 0.1 × 9.8 × 10⁻³ N

⇒ 0.1 g F = 9.8 × 10⁻⁴ N

⇒ 0.1 g F = 9.8 × 10⁻⁴ N

∴ We got the value of force in S.I units.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From coulomb's law we know,

⇒ F = (1 / 4 π ε₀) × (q₁ q₂ / r²)

Where,

• F Denotes Electrostatic force of repulsion.
• ε₀ Denotes Permmittivity of free space.
• q₁ Denotes Charge.
• q₂  Denotes Charge.
• r Denotes Distance.

Now,

⇒ F = (1 / 4 π ε₀) × (q₁ q₂ / r²)

Substituting the values,

∵ [ q₁ = q₂ = q ]

⇒ 9.8 × 10⁻⁴ = (1 / 4 π ε₀) × (q × q) / (3 m)²

⇒ 9.8 × 10⁻⁴ = (1 / 4 π ε₀) × q² / 9 m²

We Know,

1 / 4 π ε₀ has an equivalent value of 9 × 10⁹

Substituting,

⇒ 9.8 × 10⁻⁴ = 9 × 10⁹ × q² / 9

⇒ 9.8 × 10⁻⁴ = 10⁹ × q²

⇒ q² = 9.8 × 10⁻⁴ / 10⁹

⇒ q² = 98 × 10⁻⁵ / 10⁹

⇒ q² = 98 × 10⁻⁵⁻⁹

⇒ q² = 98 × 10⁻¹⁴

⇒ q = √ 98 × 10⁻¹⁴

⇒ q = 10⁻⁷ × √ 98

⇒ q = 10⁻⁷ × 9.89

⇒ q = 9.89 × 10⁻⁷

⇒ q ≈ 9.9 × 10⁻⁷ C

∴ The Magnitude of the charges (q) is 9.9 × 10⁻⁷ C.

$\rule{300}{1.5}$

Answer 2

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$</p><ul><li>\tt{\red{Given \: - }}$

• Force of attraction (F) = 0.1 g F

• Distance of separation (r) = 3 m.

___________

Assuming that the two charges each have a magnitude of Q;

___________

$</p><p>\tt{\orange {Step-By-Step-Explaination \: - }}$

Converting the values to SI Units ;

⇒ 0.1 g F = 9.8 × 10⁻⁴ N

$</p><p>\tt{\purple{F = \dfrac{1}{4 \pi \e_{0} } \times \dfrac{q_{1} q_{2} }{{r}^2} }}$

• F Denotes Electrostatic force of repulsion.

• q₁ Denotes Charge.

• q₂ Denotes Charge.

r Denotes Distance.

Substituting the values, and solving we get :

The Magnitude of the charges (q) is 9.9 × 10⁻⁷ C.