Chapter 7, Problem 33Q

To determine

The ranking of the force on each point charges $q_1$ and $q_2$ in the given pairings from the most attractive to most repulsive. The separation, d, between each pair is given. Explain the reasoning you used to arrive at your rankings.

Pair $1:q_1=+2\text{ µC};q_2=-4\text{ µC and }d=10\text{ cm}$ Pair $2:q_1=+2\text{ µC};q_2=-2\text{ µC and }d=5\text{ cm}$ Pair $3:q_1=+3\text{ µC};q_2=+3\text{ µC and }d=10\text{ cm}$ Pair $4:q_1=-5\text{ µC};q_2=-2\text{ µC and }d=20\text{ cm}$.

Answer to Problem 33Q

$\begin{array}{l}\text{Pair }2:F=14.4\text{ N; attractive}\hfill \\ \text{Pair }1:F=7.2\text{ N; attractive}\hfill \\ \text{Pair }4:F=2.25\text{N; repulsive}\hfill \\ \text{Pair }3:F=8.1\text{ N; repulsive}\hfill \end{array}$.

Explanation of Solution

Given:

Pair $1:q_1=+2\text{ µC};q_2=-4\text{ µC and }d=10\text{ cm}$ Pair $2:q_1=+2\text{ µC};q_2=-2\text{ µC and }d=5\text{ cm}$ Pair $3:q_1=+3\text{ µC};q_2=+3\text{ µC and }d=10\text{ cm}$ Pair $4:q_1=-5\text{ µC};q_2=-2\text{ µC and }d=20\text{ cm}$

Concept Used:

Force between two charges is given by Coulomb’s law:

$F=K\frac{q_1\times q_2}{d^2}$

Where, $K=9\times {10}^9{\text{Nm}}^{\text{2}}{\text{C}}^{\text{-2}}$.

Calculation:

Substitute the given values in the formula $F=K\frac{q_1\times q_2}{d^2}$, we get

Pair $1:F=(9\times {10}^9)\times \frac{2\times {10}^{-6}\times 4\times {10}^{-6}}{{\left(10\times {10}^{-2}\right)}^2} =7.2\text{ N};$ attractive force (since the charges have opposite sign)

Pair $2:F=9\times {10}^9\times \frac{2\times {10}^{-6}\times 2\times {10}^{-6}}{{\left(5\times {10}^{-2}\right)}^2}=14.4\text{ N}$ ; attractive force (since the charges have opposite sign)

Pair $3:F=9\times {10}^9\times \frac{3\times {10}^{-6}\times 3\times {10}^{-6}}{{\left(10\times {10}^{-2}\right)}^2}=8.1\text{ N}$ ; repulsive force (since the charges have same sign)

Pair $4:F=9\times {10}^9\times \frac{5\times {10}^{-6}\times 2\times {10}^{-6}}{{\left(20\times {10}^{-2}\right)}^2}=2.25\text{ N}$ ; repulsive force (since the charges have same sign)

So, the order is: pair $2$ - pair $1$ - pair $4$ - pair $3$.

Conclusion:

The order from the most attractive to most repulsive is: pair $2$ - pair $1$ - pair $4$ - pair $3$.