The last minute revisioner given below covers the salient points of the relevant sections from the exam point of view . It’s not meant to be a comprehensive review of the entire chapters.

- Charge is an
*intrinsic*( it’s own ) ,*individualistic*and*indestrucible*property of a body/particle*which results in electric forces*. No of charges can be reduced or increased by friction , conduction or induction. Charges are*quantized , conserved and additive*. A non-accelerated moving charge also causes magnetic forces in addition to the electric forces. If it’s accelerated , the charge also radiates energy. - The dielectric constant ( K =
**ε**_{r}**= ε /εo**) in Couloumb’s law is usually**≥ 1**. When a charge is placed in a medium , the force decreases K times. Coulomb’s law a)*applies only to point charges b) obeys Newton’s third law c) is not applicable to distances below***10**^{-15 }[ – fifteen ] m*and d) follows the superposition principle*. Note that the interaction between two charges is not influenced by a third charge . - The period of revolution of a particle of mass m of charge – q1 moving around a fixed charge + q2 in a circular path of radius r is given by
**T = √ ( 16 π³ εo m r³ / q1 q2 )** - Consider a thin fixed ring of radius a having a positive charge q uniformely distributed over it . Now , if a particle of mass m and having a negative charge Q is placed on the axis at a distance of x ( x << a ) from the ring’s centre , the negative charge undergos oscillatory motion nearing simple harmonic as the restoring force is not linear.
**T = √ 2 π ( 4 π εo m a³ /q Q )** - To keep the original charge distribution unchanged ,
*test charges are usually of a small value*. If a test charge doesn’t experience a force at a point , the net electric feild at that point should be zero. Note that a charged particle is not affected by it’s own feild. - Electric feild lines helps us to visualize the nature of electric feild in a given space. They a)
*never cross each other*b)*never form closed loops and*c)*doesn’t pass*. Eventhough the tangent to the line of force in an electric feild at a point gives the direction of force / acceleration acting on a positive charge at that point ,**through**a conductor*it isn’t necessary*that the charge will move in the said direction of force. - The maximum value of electric feild of a ring shaped conductor having radius r ,carrying a total uniformely distributed charge Q at a point P which lies on the axis of the ring at a distance x from it’s center is
**1/4 π εo ( 2Q /[ 3 √ 3 R² ] )** - The electric feild produced by an infinite plane sheet of charge is
*independent of the distance*from the sheet . This feild is uniform and it’s direction is perpendicular to the sheet and away from it. - The net electric feild of a linear charge / charged ring / semicircular charge and a circular charged arc is
**∫ d E cos θ .**The net electric feild of a charged rod of fixed length having charged density λ along x axis is**λ /****4 π εo ro ( sin θ1 + sin θ2 )**and along y axis is**λ /****4 π εo ro ( cos θ1 – cos θ2 ) ,**of a semicircular ring having charge density λ – x axis**λ**/**2 π εo r**and along y axis is zero , of a quarter circular ring of charge density λ – x axis and y axis is**λ**/**4 π εo r.** - Electric feild intensity of a short dipole at some general point is [
**p /****4 π εo r³ ] √ (1 + 3 cos² θ ) .**Here the resultant feild intensity vectors**E2 / E1 = tan Φ** - Electric flux through a surface describes whether electric feild points into or out of the surface. In an uniform feild , the flux through a closed surface is zero. For a surface of area A tilted at an angle Φ , flux is
**E A cos Φ**and volume flow rate through A is**dV/ dt = v A cos Φ**. - Gauss’s law is most useful in dealing with
*charge distributions of spherical / cylindrical symmentry*or when*charge distribution is uniform over a plane*. For point / spherical charge distributions gaussian surface is spherical while that for a line of charge it’s cylindrical. For feild of a line charge it’s**1 / 2 π εo ( λ/r ) ,**for an infinite plane sheet of charge**σ / 2****εo**and at the surface of a conductor it’s**σ / εo ,**inside a uniformely charged sphere**ρ r / 3****εo**and outside is (**1/4π****εo ) ( Q / r² )**. Electric feild of a long uniformely charged cylinder is**ρ R²**/**2****εo r**and that inside a uniform volume charged plane is**ρ r**/**εo**and that of the outside is (**ρ**/**εo ) d/2** - The work done by an electric force to move a point charge through a small displacement dl depends
*only on the change in the distance dr between the charges*( i.e , the end points are important*and not the path taken*), which is the radial component of the displacement. Hence the force acting is conservative. The potential energy**U**=**1/4π****εo (q qo/r ) .** - Electric potential is a
*scalar quantity*where the*principle of superposition*can be applied . This means that for a*discrete distribution of charges*where V = V1 + V2 + V3 +… , = (**1/4π****εo ) Σ q/r .**In case the potential is caused by a*continuous charge distribution*, then ,**V = ∫ dq /4π****εo .** - Equipotential surfaces can be volumes , surfaces or lines . Note –
*a) they will never cross each other as the potential at a point can’t have two values b) for rest charges , the conducting surfaces are always equipotential c) equipotential surfaces are always perpendicular to the electric lines of force and d) the work done in moving a charge from a point to another point in an equipotential surface is zero.* - The cartesian components of electric feild w.r.t the electric potential are
**Ex = – ∂V/∂x**,**Ey = – ∂V/∂y**and**Ez = – ∂V/∂z**. Note – the equation indicates that the*negative of the rate of change of potential with position in any direction is the component of E in that direction*. Negative sign means that E is pointing in the direction of decreasing V. - For an infinite rod , the potential at any point near the rod is infinite . But the potential difference between any two points a and b is
**Va -Vb = ( λ / 2 π εo ) In ( b/a ) .**