Question

a charged sphere feels a force of 53n due to a charged van de graaf generator located nearby. if the distance between the objects increases by a factor of 9, how much force will the sphere experience? type only numbers in the answer box and use standard unit abbreviations for the unit box. show your work on paper and submit at the end of the assignment to receive full credit. your answer:

Explanation:

Step1: Recall Coulomb's Law

The electrostatic force between two charged objects is given by $$F = k\frac{q_1q_2}{r^2}$$, where $k$ is Coulomb's constant, $q_1,q_2$ are the charges, and $r$ is the distance between them.

Step2: Analyze force-distance relationship

When distance $r$ increases by a factor of 9, the new distance $r' = 9r$. Substitute into the force formula:
$$F' = k\frac{q_1q_2}{(r')^2} = k\frac{q_1q_2}{(9r)^2} = k\frac{q_1q_2}{81r^2}$$

Step3: Relate new force to original force

Since $F = k\frac{q_1q_2}{r^2}$, substitute into the new force equation:
$$F' = \frac{F}{81}$$

Step4: Calculate new force

Substitute $F=53\,\text{N}$ into the equation:
$$F' = \frac{53}{81} \approx 0.65\,\text{N}$$

Answer:

$0.65\,\text{N}$