A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The electric force $F_e$ between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by the Coulomb's law:

$$F_e = k\frac{q_1q_2}{r^2}$$

where $k$ is the Coulomb constant.

In this case, we have:

$q_1 = 1.0\ C$

$r = 15\ m$

$F_e = 1.0\ N$

We need to find $q_2$. We can rearrange the above equation to solve for $q_2$:

$$q_2 = \frac{F_er^2}{kq_1}$$

Substituting the values:

$$q_2 = \frac{(1.0\ N)(15\ m)^2}{(8.99	imes10^9\ N\cdot m^2/C^2)(1.0\ C)} \approx 25	imes10^{-9}\ C = 25\ nC$$

Therefore, the answer is (E) 25 nC.

A 10-C Point Charge Is 15 M from a Second Point