IIT JEE Main / Advanced Physics 2018 – Electricity : Last Minute Revisioner [ LMR] / Cheat Sheet

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 = εr = 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 through a conductor. 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 , 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 λ4 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 R²2 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 ) .

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