Theory of VOLTAGE/POTENTIAL DIFFERENCE

Voltage Theory

Let us consider two parallel plates, which are connected to a battery. The upper plate is connected with positive terminal of a battery hence this plate is positively charged and lower plate is connected with negative terminal of the battery and hence this, lower plate is negatively charged.

These plates produce an electric field between them which is proportional to surface charge density of both plates. Let's the surface charge density of the upper plate is σ. Then surface charge density of lower plate will be - σ. The electric field produced by only positive plate is surface charge density divided by twice of permeability of the space between the plates i.e.

σ

2εo.

Similarly electric field produced by only negative plate is

−	σ
	2εo.

Hence resultant electric field between the plates is

σ	− (	− σ	) =	σ
2εo		2εo		εo

Let us now assume a positively charged particle enters into that electric field. If the particle has a charge of q Coulomb, then electrostatic force applied on that particle will be

F_e = q.E
Where E is the electric field vector and it is constant for an uniform electric field.

Now acceleration of the particle,

Fe	=	q	.E
m		m

Where m is the mass of the particle.

Hence velocity of the particle at any instant t can be written as,

v(t) = vo + ∫(	q	).E.dt
	m

Where v_o is the initial velocity of the particle at entrance into uniform electric field.

v(t) = vo +	q	.E.t
	m

So, position of the particle at any instant t can be written as,

	∫
p(t) = po +		v(t).dt

Where p_o is the initial position of the particle at entrance into uniform electric field

p(t) = po + ∫{vo + (	q	).E.t}.dt
	m

p(t) = po + vo.t +	q	.E.t2
	2m

This is a function of parabola hence it can be predicted from the function that the motion of charged particle in an uniform electric field is projectile motion in parabolic path.

Electrical Potential Difference and Definition of Voltage

We can use electric field vector to characterize electric field in a space. By observing the movement of charge particles inside an electric field one can predict the exact characteristics of that field. If field is strong enough the deflection of charged particle in parabolic path will be more sharp and if the field is weak, deflection is less. But it is not the practical way of measuring the intensity of an electric field. Another physical quantity is there which is much easier to measure and also used to characterize an electric field and this quantity is known as electric potential difference.

Electrical potential V(t) of a position in the electrical field is such that, electric potential energy required to place a particle of charge q at that position would be the product of charge of the particle q and the potential of that position V(t). That is potential energy U(t) = q.V(t).

The SI unit of electrical potential is Volt after name of Italian physicist Alessandro Volta (1745 - 1827).

Voltmeter is used to measure the potential difference between two points.

There is a misconception about potential and voltage. Many of us think that both are same. But voltage is not exactly potential it is the measure of electric potential difference of tow points.

Electrical Potential and Electrical Field vector

Electrical Potential and Electrical Field vector both characterize the same thing that is space of electrical field. Since both electric potential and electrical field vector describe an electric field, they are related.

dV = - E.ds where dV is the potential difference between tow points separated by a distance ds and electrical field vector is E.

Definition of potential difference or voltage

After going through the above portion of voltage theory we can now establish a definition of potential difference, definition of voltage in few words. Which says " Voltage is the difference in electric potential energy per unit charge between two points. Voltage is the work to be done, upon an unit charge to move between two points , against a static electric field. A voltage which is a measure of electric potential difference is the cause of current to flow in a closed circuit."

PIYUSH PUSHKAR