Physics, Electric Field

ELECTRIC FIELD IMPORTANT CONCEPTS TO REMEMBER 1. An electric field exists in a region if a charged body placed in that region experiences a force. (Repulsive or Attractive) 2. Every electric charge has electric field around it which theoretically extends to infinity. But the effect of electric field decreases quickly as the distance from the charge is increased. 3. Electric field intensity (E) at a point is the electric force (F) that acts on a small positive charge (q0) placed at that point divided by the magnitude of the small positive charge, i.e. E=F/q0 S.I unit of E is V/m or N/V. The positive charge q0 is called test charge because it is used to detect the presence of electric field. 4. Electric field intensity is a vector as it has magnitude as well as direction. The direction of electric field at a point is that of force on q0 placed at that point. 5. The terms used for E are electric field or electric field intensity or electric field strength. 6. The magnitude of force (F) on a charge q placed in an electric field of magnitude E is, F=qE Newton. 7. The magnitude of electric field E due to a point charge q at a distance r from the charge is E= (1/4ΠЄ) (q/r2) = 1/ (4ΠЄ0Єr) (q/r2) = 9 x 109(q/r2) As 1/4ΠЄ0 = 9 x 109

8. For a negative charge, the direction of electric field is radially inward; it is radially outward for a positive charge. 9. Electric field lines are used to describe the electric field in any region of space. They start from the positive charge and end on the negative charge. Two electric field lines never cross each other. The direction of E is always tangent to the electric field line at every point. 10.A charged particle of mass m and charge q moving in an electric field of magnitude E has an acceleration ‘a’ given by, a = (qE)/m . If electric field is uniform, then acceleration is constant. 11. The electric field (E) at a given point due to a number of charges (q1, q2, q3, q4…….) can be found by using superposition principle. The resultant electric field (E) is equal to the vector sum of all the electric fields of all the charges at a point. Or, E = E1 + E2 + E3 + E4 + …… where E1 is field due to q1, E2 is field due to q2 and so on. 12. The magnitude of electric field at a point P on the axis of a uniformly charged ring is, E= qx / [4ΠЄ0 (r2 + x2)3/2] Where x= distance of point p from the center of ring, q = charge on the ring, r= radius of the ring. (a) When point P lies at the center of the ring, x = 0, so E = 0. (b) When point P lies far away from the ring (x>r), we can neglect r2 as compared to x2 So, E = (1/4ΠЄ0) (qx / [x2]3/2) = (1/4ΠЄ0) (q / x2) This gives the electric field due to a point charge, so at a large distance from the ring, the ring behaves as a point charge.

13. A system of two equal and opposite charges (q, -q) separated by a small distance is called an electric dipole. The magnitude of dipole moment is equal to the product of either charge or distance between the charges. P = q x 2a or ‫ ׀‬p ‫ = ׀‬q x 2a, where 2a is equal to separation between q and – q. The dipole moment is directed from – q to q. so the dipole moment is a vector. 14. Many molecules behave as electric dipole. For e.g. HCl molecule behaves as an electric dipole. The hydrogen part of the molecule is positively charged, while chlorine part is negatively charged. 15. Magnitude of electric field intensity at point P on the axial line of the electric dipole is ‫ ׀‬E ‫ ׀ = )׀‬P 4 / (‫׀‬ΠЄ0 . (2x) / [x2 – a2]2 Then direction of E is along dipole axis from -q to +q. Here 2a is the distance between -q and +q, x is the distance of point P from the center of the dipole. For a short dipole, ‫ ׀‬E ‫ ׀‬α 1/x3 16. The magnitude of electric field intensity at point P on the equatorial line of the electric dipole is ‫ ׀‬E ‫ ׀ = ) ׀‬P 4 / ( ‫׀‬ΠЄ0[x2 + a2]3/2 The direction of ‫ ׀‬E ‫ ׀‬is parallel to dipole axis from +q to – q. x is the distance of point P from the center of dipole.

17. The electric field of a short dipole decreases as 1/x3 rather than as 1/x2 as found for a point charge. So, electric field at large distance from the dipole is negligible in comparison with the electric field of a single point charge. 18. When an electric dipole is placed in an electric field, it tends to align in the direction of electric field. 19. Let an electric dipole be placed in a uniform electric field E in such a way that its dipole moment makes an angle θ with the direction of the field. The magnitude of torque on the dipole is τ = pEsinθ. When θ=00, τ= 0. When θ = 900, torque is maximum, and is equal to pE. 20. A dipole in a uniform field experiences only torque but no force. 21. When a dipole is placed in a non uniform electric field, there is net force acting on the dipole in addition to the torque tending to align the dipole in the direction of the field. **********************************************