02(T)%20-%20Electrostatic%20Potential%20and%20Capacitance

02(T)%20-%20Electrostatic%20Potential%20and%20Capacitance -...

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2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 2.1 Line Integral of Electric Field If a unit positive charge is displaced by dl in an electric field of intensity E , work done is `given by dW = E . dl Line integration of this equation gives the work done in displacing a unit positive charge from P to Q as W = dl Q P E This work depends only on the initial and final positions of the unit charge and not on the path followed by it. Hence, work done in moving a charge along a closed path is equal to zero. Thus electric field like gravitational field is a conservative field. 2.2 Electrostatic Potential The work done by the electric field in moving a unit positive electric charge from an arbitrarily selected reference point θ, , , which may be inside or outside the field, to point P is given by W P = dl P E θ For the selected reference point, the value of W P depends only on the position of point P and not on the path followed in going from reference point to point P. Let θ be at infinity. The electric field at infinite distance due to finite charge distribution will be zero. The electric field due to an infinitely long charged plane at infinite distance will not be zero. However, in practice, one cannot have such a charge distribution. The work done in a direction, opposing the electric field in bringing a unit positive charge from an infinite position to any point in the electric field is called the static electric potential ( V ) at that point. Its sign is taken as negative as the work done is in a direction opposite to the electric field. Thus, work done in bringing a unit positive charge from infinity to points P and Q will be V ( P ) = - dl P E and V ( Q ) = - dl Q E V ( Q ) - V ( P ) = - dl Q E + dl P E = dl P E + dl Q E = - dl Q P E This equation gives the electric potential of point Q with respect to point P. Its unit is volt ( joule / coulomb ) denoted by V and its dimensional formula is M 1 L 2 T - 3 A - 1 .
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2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 2 2.3 Electric Potential Energy and Potential Difference A stationary electric charge at infinity has no energy ( kinetic or potential ) associated with it. If a unit positive charge is brought from infinity to an arbitrary point P in the electric field such that it has no velocity at that point then, the field being conservative, work done on it is stored with it in the form of potential energy and is called the electric potential of the point P and is given by V ( P ) = - dl P E If the electric charge is of magnitude q instead of unity, then the work done is called the potential energy of the charge q at point P and is given by U ( P ) = qV ( P ) = - dl P E q The original electric field or the arrangement of charges in the field should remain unaffected
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02(T)%20-%20Electrostatic%20Potential%20and%20Capacitance -...

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