A 72 nC charge is located at x = 3.00 m on the x-axis and an 8.0 nC charge is located at x = 7.0 m. At what point on the x-axis is the electric field zero?
A) −9.0 m
B) 4.0 m
C) −5.0 m
D) 6.0 m
E) 6.3 m

Question

Quizplus · Accepted Answer

The electric field due to a point charge is given by $E=k\frac{q}{r^2}$, where $k$ is Coulomb's constant, $q$ is the charge, and $r$ is the distance between the charge and the point where the electric field is being measured.

At the point where the electric field is zero, the contributions to the electric field from each charge must be equal in magnitude and opposite in direction. Let the point where the electric field is zero be at $x$. Then we have:

$$k\frac{72 	ext{ nC}}{(x-3.00 	ext{ m})^2} = k\frac{8.0 	ext{ nC}}{(7.0 	ext{ m} - x)^2}$$

Simplifying this equation, we get:

$$(x-3.00 	ext{ m})^2 = 81(7.0 	ext{ m} - x)^2$$

Expanding the right side and simplifying, we get:

$$50x^2 - 700x - 2264 = 0$$

Solving for $x$ using the quadratic formula, we get $x \approx 6.0	ext{ m}$ or $x \approx -0.045	ext{ m}$. The negative solution is extraneous because it is not in the range of the original problem. Therefore, the best choice is D: 6.0 m.

A 72 NC Charge Is Located at X = 3