Question

forces at a distance review

1. students are investigating the electric fields created by two charged objects (a and b). both objects are the same distance, d from the small positive test charge placed at point x.

image of object a (+2) separated by distance d from point x, and point x separated by distance d from object b (+1)
which way will the test charge be pushed?
a toward object a because the electric field of object b is stronger
b toward object b because the electric field of object a is stronger
c toward object a because the electric field of object b is weaker
d toward object b because the electric field of object a is weaker

Explanation:

Step1: Recall electric field formula

Electric field from a charge: $E = k\frac{Q}{r^2}$, where $k$ is constant, $Q$ is charge, $r$ is distance.

Step2: Compare fields at point x

For object A ($Q=+2$, $r=d$): $E_A = k\frac{2}{d^2}$; for object B ($Q=+1$, $r=d$): $E_B = k\frac{1}{d^2}$. So $E_A > E_B$.

Step3: Determine force direction

Positive test charge is repelled by positive charges. $E_A$ (from A to x) pushes test charge toward B; $E_B$ (from B to x) pushes toward A. Since $E_A > E_B$, net force is toward B.

Answer:

B. toward object B because the electric field of object A is stronger