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

In the given figure three point charges are situated at the corners of an equilateral triangle of side $10 cm$ . Calculate the resultant force on the charge at $B$ . What is its direction?

Accepted Answer

Given, Charge at $A$ , $q_{A} = 100 μC = 10^{- 4} C$ ,

Charge at $B$ , $q_{B} = - 100 μC = - 10^{- 4} C$

Charge at $C$ , $q_{C} = - 100 μC = - 10^{- 4} C$

Also, $A B = A C = C B = 10 cm = 10 \times 10^{- 2} m$

Force on charge at $B$ due to charge at $A$

$F_{1} = k \frac{|q_{B}| |q_{A}|}{{(A B)}^{2}} = 9 \times 10^{9} \frac{10^{- 4} \times 10^{- 4}}{{(10 \times 10^{- 2})}^{2}} = 9000 N$ along $B A$

Force on charge at $B$ due to charge at $C$

$F_{2} = k \frac{|q_{B}| |q_{C}|}{{(C B)}^{2}} = 9 \times 10^{9} \frac{10^{- 4} \times 10^{- 4}}{{(10 \times 10^{- 2})}^{2}} = 9000 N$ along $B D$

Magnitude of resultant force on charge at $B$

$F_{net} = \sqrt{{(F_{1})}^{2} + {(F_{2})}^{2} + 2 F_{1} F_{2} \cos θ}$

where, $θ$ is angle between directions $B A$ and $B D$

Since, $|F_{1}| = |F_{2}|$ , therefore

$F_{net} = \sqrt{2 {(F_{1})}^{2} + 2 {(F_{1})}^{2} \cos 120} = F_{1}$

$\Rightarrow F_{net} = 9000 N$

Now, direction of resultant force is given by,

$α = \tan^{- 1} \frac{F_{1} \sin θ}{F_{2} + F_{1} \cos θ} = \tan^{- 1} \frac{9000 \sin 120}{9000 + 9000 \cos 120}$

$\Rightarrow α = \tan^{- 1} \sqrt{3} = 60^{o}$

Hence, direction of resultant force is $60^{o}$ from horizontal line $B D$ .

In the given figure three point charges are situated at the corners of an equilateral triangle of side $10 cm$ . Calculate the resultant force on the charge at $B$ . What is its direction?

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

In the given figure three point charges are situated at the corners of an equilateral triangle of side 10cm . Calculate the resultant force on the charge at B. What is its direction?

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

In the given figure three point charges are situated at the corners of an equilateral triangle of side $10 cm$ . Calculate the resultant force on the charge at $B$ . What is its direction?