Forces between Multiple Charges

A spark or crackling sound happens when we remove synthetic clothes or sweaters from our bodies, especially in dry weather. The release of electric charges that have accumulated as a result of rubbing insulating surfaces causes this. In action, this is the force between multiple charges.

Static is a term used to describe anything that does not move or change over time. Electrostatics is the study of forces, fields, and potentials generated by static charges.

What is the Formula for Calculating the Magnitude of a Force Between Two Charges?

Coulomb’s law allows us to calculate the force between any two charges. According to Coulomb’s law, two charged things will attract or repel each other with a force comparable to the product of their masses. 

Let’s make an equation out of this, shall we?

F= K Q1Q2/d²

Depending on the charges, F is the force of attraction or repulsion.

K is the coulomb’s constant, for air it is 9×109 kg⋅m3⋅s-2⋅C-2.

Q1 and Q2 are the magnitudes of two charges

The distance between the two charges is denoted by d.

Note: Coulomb’s law states that the force between numerous charges is always applied centrifugally over a straight line connecting the charged particles’ centres.

Coulomb’s Law

The law governing the force between electric charges is known as Coulomb’s law. When the size of charged bodies is significantly lower than the distance between them, the size is ignored or not taken into account. Point charges can be applied to the charged bodies. Coulomb investigated the force between two point charges and discovered that it is inversely proportional to the square of their distance, directly proportional to the product of their magnitudes, and acting in a line connecting them.

Coulomb’s Law in Vector Form

Since force is a vector quantity, Coulomb’s law in vector form is stated very well. The position vectors for charges q1 and q2 are r1 and r2, respectively. Force on q1 due to q2 is denoted by F12, whereas force on q2 due to q1 is denoted by F21. The two-point charges q1 and q2 have been given the numbers 1 and 2 for convenience, and the vector leading from 1 to 2 has been given the number r21.

By the Principle of Superposition, What is the Force Between Multiple Charges?

In 1753, Daniel Bernoulli proposed the superposition concept.

According to the superposition principle, the net reaction of two or more stimuli is the linear sum of the individual stimuli’s responses.

For a linear function F(x), according to the principle of superposition,

F( x1 + x2 ) = F( x1 ) + F( x2), law of additivity

According to Coulomb’s equation between many charges, the cumulative electrostatic force exerted on a static charged particle by two or more static charged particles is identical to the scalar totality of individual forces placed on that particle. 

The forces between several charges using the principle of superposition are calculated as follows:

Fnet= F1 + F2 + F3 + … Fn

Where Fnet is the total electrostatic force on a particle in a system of n particles, and F1, F2, F3… are the electrostatic forces on the particles in the system. The forces exerted by particles 1, 2, 3… n is denoted by Fn.

The principle of superposition is a very powerful and helpful technique.

Limitations of Coulomb’s Law

Coulomb’s Law, for calculating the forces between multiple charges by the principle of superposition, cannot be applied freely because it is based on specific assumptions. The following are some of Coulomb’s law’s limitations:

• The formula can only be used to calculate static charges (which are in rest position).
• When the charges are in an irregular shape, applying Coulomb’s law is more difficult since determining the distance between them is challenging. The law, on the other hand, can be easily applied to regular shapes.
• Coulomb’s formula is only true when the solvent molecules between the charged substances are greater than both of them.
• On large planets, the law cannot be simply applied to find the charge.

How to solve problems on Coulomb’s Law?

The procedures to solving problems with Coulomb’s Law are as follows:

• Evaluate whether the charge’s force is attractive or repulsive, and depict it by drawing a vector pointing towards or away from the charge, as appropriate.
• Using Coulomb’s Law, calculate the magnitude of force (without considering the signs of charges).
• Using the specified coordinate axes, solve the forces and represent them in vector form using the I j, and k unit vector notation.
• Use the principle of superposition to calculate the charge’s net force.

When to Apply Coulomb’s Law?

Coulomb’s law can be used in the following situations.

• To determine the distance between two-point charges or the force between them.
• To determine the force exerted on a single point as a result of multiple other point charges.
• To figure out how strong the electric field is. Coulomb’s Law can be used to calculate the electric field as follows:

E = F/Q

Where E refers to the strength of Electric Field

F = Electrostatic Force

Q = Test charge in Coulomb’s

Conclusion 

The total force acting on a charged body in the vicinity of other charges is the algebraic sum of each force acting on it by other charges. This force can be calculated by applying Coulomb’s law on each pair. 

Here, we’ve learned the nature of this force and the appropriate way of calculating it using the Coulomb’s law force between multiple charges and the principle of superposition.