Name: Forces Between Multiple Charges
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: To find the force on a charge due to multiple charges by applying the superposition principle, we need to know the basic concepts first. Watch the video to l...

Question

Three-point charges $q, - 4 q$ and $2 q$ are placed at the vertices of an equilateral triangle ABC of side $l$ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $q$ .

Accepted Answer

The forces acting on the charge $q$ are due to the other two charges,

The force at A due to charge at C, $F_{1} = \frac{k q (2 q)}{l^{2}} = \frac{2 k q^{2}}{l^{2}}$

The force at A due to charge at B, $F_{2} = \frac{k q (- 4 q)}{l^{2}} = \frac{- 4 k q^{2}}{l^{2}}$

The forces acting on charge $q$ can be broken into components as shown in the figure below:

Resolving the forces along the x and y- directions.

We can calculate the net force along the x-axis:

$F_{x} = - F_{1} \cos (60 °) + F_{2} \cos (60 °) \hat{x}$

$F_{x} = - \frac{k 2 q^{2}}{l^{2}} . \frac{1}{2} - \frac{k 4 q^{2}}{l^{2}} . \frac{1}{2} \hat{x} = - \frac{3 k q^{2}}{l^{2}} \hat{x}$

The net force along the y-axis:

$F_{y} = - (F_{2} \sin (60 °) - F_{1} \sin (60 °)) \hat{y}$

$F_{y} = - \frac{k 4 q^{2}}{l^{2}} . \frac{\sqrt{3}}{2} + \frac{k 2 q^{2}}{l^{2}} . \frac{\sqrt{3}}{2} \hat{x} = - \frac{\sqrt{3} k q^{2}}{l^{2}} \hat{y}$

Thus, the net force acting on the charge,

$F_{n e t} = F_{x} + F_{y}$

$F_{n e t} = - \frac{3 k q^{2}}{l^{2}} \hat{x} - \frac{\sqrt{3} k q^{2}}{l^{2}} \hat{y} = - \frac{k q^{2}}{l^{2}} (3 \hat{x} + \sqrt{3} \hat{y})$

Three-point charges $q, - 4 q$ and $2 q$ are placed at the vertices of an equilateral triangle ABC of side $l$ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $q$ .

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

Three-point charges q, –4q and 2q are placed at the vertices of an equilateral triangle ABC of side l as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

Three-point charges $q, - 4 q$ and $2 q$ are placed at the vertices of an equilateral triangle ABC of side $l$ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $q$ .