Question

Three point charges lie along a straight line as shown in the figure below, where q1 = 5.94 µC, q2 = 1.41 µC, and q3 = -2.2 µC. The separation distances are d1 = 3.00 cm and d2 = 2.00 cm. Calculate the magnitude and direction of the net electric force on each of the charges.

Answer 1

Concepts and reason

The concepts used to solve this problem is electric field magnitude and direction.

Initially, the principle to be applied to this question is the “Principle of Superposition”. Applying this principle on each of the charges, to find out the magnitude and direction of the force on the charge due to the other two charges.

“Coulomb’s Law” is to be used to find the magnitude of the electric force between the charges. From the expression of the Coulomb force, it depends on the charge and the distance between the charges.

Fundamentals

The principle of superposition states that the force between two charges is totally independent of the influence of the other charges. If the force on a charge say due to being and due to be and so on, then the resultant force on is

Here, is the total number of charges.

The formula for electric force is as follows:

Here, is constant and the value ofis equal to, is the magnitude of charge and is the distance between the two charges.

Calculate the magnitude of charge in between the charge and.

The expression of the magnitude of charge in between and is equal,

Here,is the force between the charge and.

Substitutefor,for,forand forin the above expression of the force.

From the above expression of the force, both charges are the same polarity, therefore, the nature of the force is repulsive.

Calculate the magnitude of charge in between the charge and.

The expression of the magnitude of charge in between and is equal,

Substitutefor,for,foranforin the above expression of the force.

From the above expression of the force, one charge has positive polarity and another charger has negative polarity. Therefore, the nature of the force is attractive.

The expression of the net force on charge is equal to,

Substitute forandfor in the above expression of the net force

The direction of the force is repulsive.

Calculate the magnitude of charge in between the charge and.

The expression of the magnitude of charge in between and is equal,

Substitutefor,for,foranforin the above expression of the force.

The resultant force on is towards the right.

The expression of the net force on charge is equal to,

Substitute forandfor in the above expression of the net force,

The expression of the net force on the charge is equal to,

Substituteforandfor in the above expression of the net force

The resultant force on is towards the left.

Ans:

The magnitude of the force on the charge it is and the direction is west.

The magnitude of the force on the charge it is and the direction is west.

The magnitude of the force on is equal to and the direction is west.