Question

13.2 Electric Force. Coulomb's Law Coulomb's Lau Firi a F12= 41 o 2f12-Note that Fi2 is the force on l by 2; and 12-71-72 points from 2 to 1.fi 7 is the unit vector in the direction of In general for multiple di rete charges, net orce on charge 1, F (Pairwise vector sum; superposition principle). For convenience, ke = 9 x 109 appropriate units. Think How is N3L applicable here? Σ in 4

Answer 1

13.2)

Charge $Q_1$ is at rest located at $\vec{r}_1$.

Charge $Q_2$ is at rest located at $\vec{r}_2$.

$\hat{r}_{12}=\frac{\vec{r}_{12}}{r_{12}}$ , $\hat{r}_{21}=\frac{\vec{r}_{21}}{r_{21}}$ , $\hat{r}_{12}=-\hat{r}_{21}$ , ${r}_{12}=r_{21}$

Force on charge $Q_1$ due to charge $Q_2$ is $\vec{F}_{12}=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{12}^2}\hat{r}_{12}$

Force on charge $Q_2$ due to charge $Q_1$ is $\vec{F}_{21}=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{21}^2}\hat{r}_{21}$

$\vec{F}_{12}+\vec{F}_{21}=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{12}^2}\hat{r}_{12}+\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{21}^2}\hat{r}_{21}$

$\vec{F}_{12}+\vec{F}_{21}=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{12}^2}\hat{r}_{12}-\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r_{12}^2}\hat{r}_{12}$

$\vec{F}_{12}+\vec{F}_{21}=0$

$\vec{F}_{12}=-\vec{F}_{21}$

Force on charge $Q_1$ due to charge $Q_2$ is equal and opposite to force on charge $Q_2$ due to charge $Q_1$. (Newton's third law)

Hence Newton's third law is applicable here.

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12)

Initially the charges on two balls are $-2Q,+8Q$, separated by a distance $d$

Force of attraction between the two balls is $F=\frac{1}{4\pi\epsilon_0}\frac{2Q*8Q}{d^2}=\frac{1}{4\pi\epsilon_0}\frac{16Q^2}{d^2}$

The two balls brought in contact, and the charge on two balls are equal, charge on each ball is $Q'=\frac{-2Q+8Q}{2}=+3Q$

Again the two balls are separated through a distance of $d$.

Force of repulsion between the two balls is $F'=\frac{1}{4\pi\epsilon_0}\frac{3Q*3Q}{d^2}=\frac{1}{4\pi\epsilon_0}\frac{9Q^2}{d^2}=\frac{9}{16}F$

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