The answer is c. +2.0 µC
To calculate this, we will use Coulomb's Law:
F = k*Q1*Q2/r²
where F is force, k is constant, Q is a charge, r is a distance between charges.
k = 9.0 × 10⁹ N*m/C²
It is given:
F = 7.2 N
d = 0.1 m = 10⁻¹ m
Q1 = -4.0 µC = 4 * 1.0 × 10⁻⁶ = 4.0 × 10⁻⁶
Q2 = ?
Thus, let's replace this in the formula for the force:
7.2 = 9.0 × 10⁹ * 4.0 × 10⁻⁶ * Q2/(10⁻¹)²
7.2 = 9 * 4 * 10⁹⁻⁶ * Q2/10⁻¹°²
7.2 = 36 × 10³ * Q2 / 10⁻²
Multiply both sides of the equation by 10⁻²:
7.2 × 10⁻² = 36 × 10³ * Q2
⇒ Q2 = 7.2 × 10⁻² / 36 × 10³ = 7.2/36 × 10⁻²⁻³ = 0.2 × 10⁻⁵ = 2 × 10⁻⁶
Since µC = 1.0 × 10^-6:
Q2 = 2 * 1.0 × 10^-6 = 2 µC
