Name: Continuous Charge Distribution
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: This video will help us understand the necessity of continuous charge distribution and learn about the concept of linear charge density. Learn more.

Question

(i) Express Coulomb's law in vector form.
(ii) Two point charges

q_{1} = 5 \times 10^{- 6} C

and

q_{2} = 3 \times 10^{- 6} C

are located at

(3, 5, 1) m

and

(1, 3, 2) m

. Find

\vec{F_{12}}

and

\vec{F_{21}}

using vector form of Coulomb's law.

Accepted Answer

(i) The Coulomb’s law of electrostatic force states that the electrostatic force of attraction and repulsion are directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges.

$\Rightarrow F \propto q_{1} \times q_{2} \Rightarrow F \propto \frac{1}{r^{2}}$

Where,

$q_{1}, q_{2}$ are the charges and $r$ is the distance between the charges

Thus, the electrostatic force is given by,

$\Rightarrow F = \frac{k q_{1} q_{2}}{r^{2}}$

Where, $k$ is the constant of proportionality

The vector form of the Coulomb’s law is given as:

$\vec{F} = \frac{k q_{1} q_{2}}{{r^{2}}_{12}} {\hat{r}}_{12}$

Here, $r_{12}$ is the displacement from charge 1 to charge 2.

The magnitude of force between charge 1 and charge 2 is equal. But in vector form force on charge 1 is given as:

${\vec{F}}_{12} = \frac{k q_{1} q_{2}}{{r^{2}}_{12}} {\hat{r}}_{12}$

Force on charge 2 is given as:

${\vec{F}}_{21} = \frac{k q_{1} q_{2}}{{r^{2}}_{21}} {\hat{r}}_{21}$

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

(ii) Here,

$q_{1} = 5 X 10^{- 6} C q_{2} = 3 X 10^{- 6} C {\vec{r}}_{2} = (3 \hat{i} + 5 \hat{j} + \hat{k}) {\vec{r}}_{1} = (\hat{i} + 2 \hat{j} + 2 \hat{k)}$

${\vec{r}}_{12} = {\vec{r}}_{2} - {\vec{r}}_{1} = (2 \hat{i} + 2 \hat{j} - \hat{k}) |{\vec{r}}_{12}| = \sqrt{{(2)}^{2} + {(2)}^{2} + {(- 1)}^{2}} = 3 m$

${\hat{r}}_{12} = \frac{{\vec{r}}_{12}}{|{\vec{r}}_{12}|} = \frac{2 \hat{i} + 2 \hat{j} - \hat{k}}{3}$

${\vec{F}}_{21} = \frac{k q_{1} q_{2}}{{r^{2}}_{12}} {\hat{r}}_{12} = \frac{9 \times 10^{9} \times 5 \times 10^{- 6} \times 3 \times 10^{- 6}}{{(3)}^{2}} \times \frac{2 \hat{i} + 2 \hat{j} - \hat{k}}{3} = 5 \times 10^{- 3} \times (2 \hat{i} + 2 \hat{j} - \hat{k}) N$

$|{\vec{F}}_{21}| = \sqrt{{(2)}^{2} + {(2)}^{2} + {(- 1)}^{2}} \times 5 \times 10^{- 3} = 1.5 \times 10^{- 2} N$

As

${\vec{F}}_{12} = {\vec{F}}_{21} = - (5 \times 10^{- 3}) \times (2 \hat{i} + 2 \hat{j} - \hat{k}) N$

(i) Express Coulomb's law in vector form.
(ii) Two point charges $q_{1} = 5 \times 10^{- 6} C$ and $q_{2} = 3 \times 10^{- 6} C$ are located at $(3, 5, 1) m$ and $(1, 3, 2) m$ . Find $\vec{F_{12}}$ and $\vec{F_{21}}$ using vector form of Coulomb's law.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

(i) Express Coulomb's law in vector form. (ii) Two point charges q1=5×10-6C and q2=3×10-6C are located at (3,5,1)m and (1,3,2)m. Find F12→ and F21→ using vector form of Coulomb's law.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

(i) Express Coulomb's law in vector form.
(ii) Two point charges $q_{1} = 5 \times 10^{- 6} C$ and $q_{2} = 3 \times 10^{- 6} C$ are located at $(3, 5, 1) m$ and $(1, 3, 2) m$ . Find $\vec{F_{12}}$ and $\vec{F_{21}}$ using vector form of Coulomb's law.