Definitions [10]
“An electric line of force is an imaginary smooth curve drawn in an electric field along which a free, isolated positive charge moves. The tangent drawn at any point on the electric line of force gives the direction of the force acting on a positive charge placed at that point.”
OR
An imaginary curve drawn in such a way that the tangent at any given point on this curve gives the direction of the electric field is called an electric line of force.
The line passing through the centre of the dipole and perpendicular to the dipole axis is called the equatorial line.
“The line joining the two charges, pointing from the negative charge to the positive charge. This is known as the ‘direction of dipole axis’.”
An electric dipole is a pair of equal and opposite point-charges placed at a short distance apart.
OR
A system formed by two equal and opposite point charges placed at a small distance apart is called an electric dipole.
The midpoint of the line joining the two charges is called the centre of the dipole.
Define electric dipole moment.
The electric dipole moment is defined as the product of the magnitude of one of the charges and the distance between the two equal and opposite charges.
The ratio of the charge Q given to one of the conductors of a capacitor to the potential difference V between the conductors is called its capacitance, given by C = Q/V.
The maximum electric field that a dielectric medium can withstand without breakdown (of its insulating property) is called its dielectric strength.
A system consisting of two conductors having equal and opposite charges separated by an insulator or dielectric is called a capacitor.
The ability of a conductor to store charge is called the capacity of conductor.
Formulae [4]
p = q × 2a
It is a vector quantity; its direction is from −q to +q.
C = Q/V
C = 4πkε₀ · [\[\frac {ab}{(b − a)}\]]
C = \[\frac {2πkε₀ l}{2.303 log(b/a)}\]
Key Points
- Electric field lines originate from positive charges and terminate on negative charges (or at infinity).
- The tangent to a field line at any point gives the direction of the electric field; in a uniform field, the lines are parallel and straight.
- No two electric field lines intersect, as this would imply more than one direction of the electric field at a point.
- Electric field lines do not pass through a conductor, showing that the electric field inside a conductor is zero.
- The density of field lines indicates field strength—closer lines represent a stronger field, while wider spacing represents a weaker field; the lines are continuous and imaginary, though the field is real.
1. Infinite Line Charge
\[E=\frac{\lambda}{2\pi\varepsilon_0r}\]
2. Infinite Plane Sheet
\[E=\frac{\sigma}{2\varepsilon_0}\]
3. Charged Conducting Plate
\[E=\frac{\sigma}{\varepsilon_0}\]
4. Spherical Shell
Inside (r < R):
E = 0
Outside (r > R):
\[E=\frac{Q}{4\pi\varepsilon_0r^2}\]
On surface (r = R):
\[E=\frac{Q}{4\pi\varepsilon_0R^2}\]
5. Charged Solid Sphere (Non-conducting)
Inside:
\[E\propto r\quad\left(E=\frac{Qr}{4\pi\varepsilon_0R^3}\right)\]
Outside:
\[E=\frac{Q}{4\pi\varepsilon_0r^2}\]
- Capacitance depends on the geometry (shape, size, separation) of the conductors and on the dielectric between them.
- In a series, the charge on each capacitor is the same, but the voltage across each is different.
- A series combination divides high voltage — the capacitor with the smallest capacitance gets the largest P.D., and it cannot store much charge.
- In parallel, the voltage across each capacitor is the same, but the charge on each is different, and it handles only low voltage.
- A parallel combination is used when a large capacitance at low potential is needed, as it can store a large amount of charge.
