4. Electric Lines of Force due to a Uniform Field: Properties of Electric Lines of Force or Field Lines: The electric lines of force are imaginary lines. A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so. 1. 2. 3. The electric lines of force emanate from a positive charge and terminate on a negative charge. 4. The tangent to an electric field line at any point gives the direction of the electric field at that point. 5. Two electric lines of force can never cross each other. If they do, then at the point of intersection, there will be two tangents. It means there are two values of the electric field at that point, which is not possible. Further, electric field being a vector quantity, there can be only one resultant field at the given point, represented by one tangent at the given point for the given line of force.

Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where the electric field is weaker. 6. 7. Electric lines of force are perpendicular to the surface of a positively or negatively charged body. 8. Electric lines of force contract lengthwise to represent attraction between two unlike charges. Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges. 9.

10. The number of lines per unit cross - sectional area perpendicular to the field lines (i.e. density of lines of force) is directly proportional to the magnitude of the intensity of electric field in that region. AN 11. Electric lines of force do not pass through a conductor. Hence, the interior of the conductor is free from the influence of the electric field. Solid or hollow conductor Electrostatic Shielding) No Field 12. Electric lines of force can pass through an insulator.

Electric Dipole: Electric dipole is a pair of equal and opposite charges separated by a very small distance. The electric field produced by a dipole is known as dipole field. Electric dipole moment is a vector quantity used to measure the strength of an electric dipole. p (q x 21) 2 1 The magnitude of electric dipole moment is the product of magnitude of either charge and the distance between the two charges. The direction is from negative to positive charge. The SI unit of p' is coulomb metre (C m)'. Note: An ideal dipole is the dipole in which the charge becomes larger and larger and the separation becomes smaller and smaller.

Electric Field Intensity due to an Electric Dipole: i) At a point on the axial line: Resultant electric field intensity at the point P is Ep=Eg-EA Ep = EA + EB The vectors EA and Ep are collinear and opposite. 2 p x 2 p x PIE Ifl << x, then X + 1)2 The direction of electric field intensity at a point on the axial line due to a dipole is always along the direction of the dipole moment 1 2 (q . 2) x 4TTE0 2 1212

ii) At a point on the equatorial line: Resultant electric field intensity at the point Q is Eg EB sin Q EAE Es cos. e The vectors EA and Ep are acting at an angle 20. EAcos E sin 4TTE (x2 +2 x2 +12 The vectors EA sin and EB sin are opposite to each other and hence cancel out. 4TTEo (x2+2) (x2+ 12 ) The vectors E, cos and EB cos are acting along the same direction and hence add up. x2 +2 )3/2 4TTE x2 +12)3/2

-2 1 4TTED(x212)32 i) Ifi << y, then EaR The direction of electric field intensity at a point on the equatorial line due to a dipole is parallel and opposite to the direction of the dipole moment. If the observation point is far away or when the dipole is very short, then the electric field intensity at a point on the axial line is double the electric field intensity at a point on the equatorial line. i.e. Ifi << x and I << y, then Ep 2 Eo

Torque on an Electric Dipole in a Uniform Electric Field: The forces of magnitude pE act opposite to each other and hence net force acting on the dipole due to external uniform electric field is zero. So, there is no translational motion of the dipole. However the forces are along different lines of action and constitute a couple. Hence the dipole will rotate and experience torque. Torque: Electric Force x distance t q E (2i sin ) = pEsin Case i: If = 0 , then t 0 . Case ii: If 90 , then t- pE (maximum value) Case iii: If -180 , then t- 0. Direction of Torque is perpendicular and into the plane containing p and E. Sl unit of torque is newton metre (Nm).

Work done on an Electric Dipole in Uniform Electric Field: When an electric dipole is placed in a uniform electric field, it experiences torque and tends to allign in such a way to attain stable equilibrium 21 W p E (cos0, cos e2) If Potential Energy is arbitrarily taken zero when the dipole is at 90, then P.E in rotating the dipole and inclining it at an angle is Potential Energy U--p E cos Note: Potential Energy can be taken zero arbitrarily at any position of the dipole. Case i: If e 0 , then U Case ii: If -90 , then U 0 Case iii: If 180 , then U- pE (Unstable Equilibrium) pE (Stable Equilibrium) END

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Manish kumar

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Thank you so much for completing geometry lessons

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