http://iit-jee-physics.blogspot.com/2008/03/concept-review-ch-29-electric-field-and.html

The charge on a proton is

e = 1.60218*10^-19 C

Coulomb's formula for the electric force between two charges.

(1) F = k*q1*q2/r²

q1,q2 charges

r = separation between charges

k = constant

In SI units k is measured to be 8.98755*10^9 N-m²/C²

The constant k is often written as 1/4πε

_{0}.

The constant ε

_{0}is called the permittivity of the space and its value is

ε

_{0}= 8.85419*10^-12 C²/N-m²

The intensity of field is defined as Vector E = Vector F/q

(3)

**E**=

**F**/q

Electric field due to a point charge (Q)

(4) E = F/q = Q/4πε

_{0}r²

(5) U(r2) - U(r1) = -W = [q1*q2/4πε

_{0}]* [(1/r2) - (1/r1)]

Choosing potential energy at infinite separation as zero

(6) U(r) = U(r) - U(∞) = [q1*q2/4πε

_{0}]* (1/r)

= q1*q2/4πε

_{0}r

(7) VB - VA = (UB - UA)/q

We can define absolute electric potential at any point by choosing a reference point P and saying that the potential at this point is zero.

(8) VA = VA - VP = (UA - UP)/q

The potential due to a point charge Q (placed at A) at a point P with distance AP = r is

(9) VP = Q/4πε

_{0}r

The electric potential at a point due to more than one charge in the system is obtained by finding potential due to individual charges and then adding them.

10. Relation between electric field and potential

dV = -

**E**.

**dr**

Integrating between limits r1 and r2

V2 – V1 = - ∫

**E**.

**dr**

If we choose r1 as infinity (reference point)

V(r) = - ∫

**E**.

**dr**(from infinity to r)

Hence we can calculate potential V if we know E and r.

If we know V we can find E through the relation

Ex = - ∂V/∂x

Ey = -∂V/∂y

Ez = -∂V/∂z

We can find the x,y and z components of E.

E can be written as Ex

**i**+Ey

**j**+ Ez

**k**

We can write dV as dV = -E dr cos θ where θ is the angle between the field E and the small displacement dr.

-dV/dr = E cos θ

15. Electric Dipole

Electric dipole moment

It is defined as a vector

**p**= q*distance vector

**d**

where distance vector is the vector joining the negative charge to the positive charge.

The line along the direction of the dipole moment is called the axis of the dipole.

16. Electric potential due to a dipole at a point P

Point is at distance r from the centre of the diploe (d/2) and theline joining the point P to the centre of the dipole make an angle θ with the direction of dipole movement (from –q to +q)

Potential at P due to charge –q = - [1/4πε

_{0}][q/(r + (dcos θ)/2)]

Potential at P due to charge q = [1/4πε

_{0}][q/(r - (dcos θ)/2)]

Net potential due to q and –q = [1/4πε

_{0}](qd cos θ)/r²

17. Electric field due to a dipole

E

_{r}= [1/4πε

_{0}](2p cos θ)/r³

E

_{θ}= [1/4πε

_{0}](p sin θ)/r³

Resultant electric field at P = E= √ (E

_{r}²+ E

_{θ}²)

= [1/4πε

_{0}](p/r³)√(3 cos²θ + 1)

19. Torque on an electric dipole placed in an electric field.

If the dipole axis makes an angle θ with the electric field magnitude of the torque = | Γ| = pE sin θ

In vector notation

**Γ**=

**p**×

**E**

20. Potential energy of a dipole placed in a uniform electric field

dipole axis makes an angle θ with the electric field magnitude of the torque

Change in potential energy = U(θ) – U(90°) = -pE cos θ = -

**p**.

**E**

If we choose the potential energy of the dipole to be zero when θ = 90° , above equation becomes

U(θ) = -pE cos θ = -

**p**.

**E**

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