Question

Four identical charged particles (q = +11.0 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 61.8 cm and W = 15.2 cm.

(a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. N

(b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. ° (counterclockwise from the +x-axis)

Please show the steps to this question, I am trying to do it and undestand it.

Answer 1

Concepts and reason

The concepts used to solve this problem are coulomb’s law, direction of force, and Pythagoras’s theorem.

First, draw the direction of electric force from all the three charges at the lower left corner. Then, use expression of coulomb’s law to find the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges.

Fundamentals

From the coulomb’s law the magnitude of electrostatic force between the two point charges is directly proportional to the magnitude of charges and inversely proportional to the square of the distance between them.

The expression for the magnitude of electrostatic force is,

Here, is the magnitude of electrostatic force, is the coulomb’s constant, is the value of charge, and is the distance between the charges.

The given bellow figure showing the electric force exerted on the charge at the lower left corner by the other three charges.

Expression for net force on charge due to the charge is,

Here, is the net force on charge due to the charge , is the component of force on charge due to the charge , and is the component of force on charge due to the charge .

Expression for net force on charge due to the charge is,

Here, is the net force on charge due to the charge , is the component of force on charge due to the charge , and is the component of force on charge due to the charge .

Expression for net force on charge due to the charge is,

Here, is the net force on charge due to the charge , is the component of force on charge due to the charge , and is the component of force on charge due to the charge .

The expression for the direction of force is,

Here, is the direction, is the vertical component of force, and is the horizontal component of force.

From the Pythagoras theorem,

Here, is the hypotenuse of right triangle, and are the adjacent sides.

(a)

The expression for the magnitude of electrostatic force is,

Expression for net force on charge due to the charge is,

…… (1)

From the figure, the expression for the force is,

Substitute for , for and , and for .

Substitute for and for in equation (1).

Expression for net force on charge due to the charge is,

…… (2)

From the figure, the expression for the force is,

Substitute for , for and , and for .

Substitute for and for in equation (2).

[Part a]

(a)

From the figure expression for is,

Substitute for and for .

Using Pythagoras theorem, using the figure the distance between the charge and is,

Here, is the distance between the charge and .

Substitute for and for .

Expression for net force on charge due to the charge is,

Substitute for and for .

Substitute for , for and , for , and for .

The magnitude of the total electric force exerted on the charge by the other three charges is,

Substitute for , for , and for .

Magnitude of the force is,

Therefore, the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges is .

(b)

The expression for the direction of force is,

Substitute for and for .

The direction of net force is,

Therefore, the direction of the total electric force exerted on the charge at the lower left corner by the other three charges counterclockwise from the +ve axis.

Ans: Part a

The magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges is .

Part b

The direction of the total electric force exerted on the charge at the lower left corner by the other three charges is counterclockwise from the +ve axis.