## ELECTRIC FIELD

Electric Field and Electric Field Intensity$\\$

• The space around an electric charge in which its influence can be experienced is known as electric field.$\\$

• The electric field intensity $\vec{E}$ at any point is equal in magnitude to the force experienced per unit (test) position charge placed at that point and is directed along the direction of the force experienced.$\\$i.e $\vec{E}$=$\frac{\vec{F}}{q}$$\vec{F}$=qE$\\$

• Electric field intensity is a vector quantity. Electric field intensity due to positive charge is always away from the charge and due to negative charge is

always towards the charge.$\\$

• Its unit is Newton/Coulomb (N$C^{-1}$)or Volt/meter (V$m^{-1}$ )$\\$
• Electric field due to point charge q at distance r is: E=$\frac{1}{4πε_0}\frac{q}{r^2} \\$
• $\vec{E}$=$\vec{E_1}$+$\vec{E_2}$+$\vec{E_3}$+ ……………$\\$
• The magnitude of the resultant of two electric fields is given by E=$\sqrt{E_1 ^2+E_2 ^2+2E_1 E_2 cos⁡θ} \\$

## Electric Lines of Force

1. The line or a curve along which an isolated +ve charge would travel if it is free to move in an electric field is known as electric line of force.

2. They start from positively charged body and end at a negatively charged body.

3. No electric lines of force exist inside the charged body.

4. Tangent to the line of force at any point gives the direction of electric intensity at that point.

5. No two electric lines of force can intersect each other.

6. The electric lines of force are always normal to the surface of a conductor, both while starting and ending on the conductor. Therefore, there is no component of electric field intensity parallel to the surface of the conductor.

7. They never form closed loops.

8. They are always perpendicular to equipotential surface.

9. The electric lines of force contract longitudinally, on account of attraction between unlike charges.

10. The electric lines of force exert a lateral pressure on account of repulsion between like charges.

11. In uniform electric field, the electric lines of force are equidistant, parallel straight lines.

12. When a metallic solid sphere is placed in a uniform electric field, then the lines of force are normal to the surface at every point but they cannot pass through the conductor.

## Field Intensity in Special Cases

1. Intensity of the electric field inside a charge spherical conductor/ hollow/ spherical shell/ conducting sphere is zero, since charge resides on the outer surface of the conductor. But $E_{surface}=\frac{1}{4πε_o} \frac{q}{R^2}$ (Where R= radius of the sphere) $E_{outside} =\frac{1}{4πε_o} \frac{q}{r^2}$ (For r>R )

2. The intensity of electric field for a uniformly charged non- conducting sphere of radius R is given by$\\$$E_{outside} =\frac{1}{4πε_o} \frac{q}{r^2}$ (For r>R )$\\$

$E_{surface}=\frac{1}{4πε_o}.\frac{q}{R^2}$ (Where r=R is radius of the sphere)$\\$$E_{inside} =\frac{1}{4πε_o}. \frac{qr}{R^3}$ ( For r<R)$\\$$E_{centre}$ = 0 ( for r=0)$\\$

3. Intensity of electric field at some point on the axis of uniformly charged ring of radius R is given by$\\$E=$\frac{1}{4πε_o}\frac{qx}{(x^2+R^2 )^{3/2}} =\frac{λRx}{2ε_o (x^2+R^2 )^{3/2}}$$\\$But it is zero at the center of ring.$\\$

4. Intensity of electric field near an infinite rod of charge is given by$\\$E=$\frac{λ}{2πε_0 r}$$\\$where λ is the linear charge density and r is the distance from the axis of rod.

5. Intensity of the electric field near a non-conducting infinite sheet of charge is E=$\frac{σ}{2ε_o}$$\\$where σ is the surface charge density.

## Electric Dipole

1. INTRO:$\\$

• Two equal and opposite charges

separated by a small distance constitute an electric dipole.$\\$

• Electric dipole moment is a vector

quantity (p) whose magnitude is equal to the product of magnitude of one charge and the distance between the two charges.$\\$

2. Do You Know?$\\$Dipole moment is a vector whose direction is from negative charge (-q) to positive charge (+q).$\\$Electric dipole moment$\\$$\vet{p}$=q.d$∴$\vet{p}\$=q(2l)

3. Electric field intensity on equatorial/ broadside on position/ Tan B position:$\\$Magnitude of electric field produced by dipole,$\\$$E_b=\frac{p}{4πε_o (r^2 + l^2 )^{3/2}}$$\\$For short dipole, r> > >d$\\$$E_b=\frac{1}{4πε_0}. \frac{p}{r^3}$ ⇒