Maximize your chance of success and high rank in JEE (Main & Advance), WBJEE, NEET. This notes specially designed column is updated year after year by a panel of highly qualified teaching expert well tuned to that Entrance Examination, Electrostatics, Electric Electric Force & Field, Electric Potential
The strength of particle's electric interaction with object around it depends on its electric charge, which can be either positive or negative. An object with equal amounts of the two kinds of charge is electrically neutral, whereas one with an imbalance is electrically charged.
In the table given below, if a body in the first column is rubbed against a body in the second column, the body in the first column will acquire positive charge, while that in the second column will acquire negative charge.
SL No. | First Column | Second Column |
---|---|---|
1 | Glass rod | Silk rod |
2 | Flannes or cat skin | Ebonite rod |
3 | Woolen cloth | Amber |
4 | Woolen cloth | Rubber shoe |
5 | Woolen cloth | Plastic objects |
Electric charge and its properties:
(1) Charge is a basic property associated with the elementary particles. It is scalar quantity.
(2) Elementary charge (e) is one of the fundamental constant with the value, value, e=−1.602×10−19C
(3) There are two kind of charges, positive and negative.
(4) Mass, length and time depend on state of rest or motion while charge is invariant (theory of relativity).
(5) Electric charge is quantised. i.e. q=ne where, n=0,±1,±2,±3,......
(6) The charge of an isolated system is conserved.
(7) Amount of induced charge ≤ inducing charge, sign of equality holds only for metals.
Coulomb's law and Factor Affecting it:
(3) If a dielectric slab (∈r) of thickness is placed between two charges kept at a distance then the electric force decreases. This reduce force is given by
(4) If for two identical charges, then F=14π∈0Q1Q2r2 where, r=d−t+t√∈r
(5) If Fg=Fe for two identical charges, then Qm=√4π∈0G
(6) When two charges Q1 and Q2 are placed some distance apart, neutral point is nearer to smaller charge and in between Q1 and Q2 if charges are alike.
(1) Coulomb's law is only applicable for point charges.
(2) Like charged bodies may attract each other
(3) Attraction also takes place between charged and neutral body.
(4) Electrostatics force of attraction in conservative in nature.
(5) The work done by electrostatics force does not depends upon path. It only depends upon initial and final positions.
(6) In a closed path work done by electrostatics force is zero i.e., ∫c→F.→dl=0
(7) Coulomb's law holds good for all distance greater than 10−15m
(8) No relativistic variation is found in electric charge.
(9) The transfer of charge without mass is not possible.
(10) The transfer of mass without charge is possible.
(11) Massless particle (e.g., photon) never be charged.
(12) Charging by induction takes place without any loss of charge from the charging body.
(13) The magnitude of induced charged is always less or equal to charging body.
(14) Electrostatics induction only takes place between bodies of definite shape (either conducting or non-conducting)
Electric field:
Electric Field Intensity in Some Particular Cases:
Charge→←\vboxto.5ex\vssElectric−Field→←\vboxto.5ex\vssCharge
First charge sets up an electric field and the second charge interacts with the electric field of the first charge.
(1) →E=→Fq0=14πε0Qr2ˆr
The direction of →E is the same as the direction of →F because the test charge q0 is a positive scalar quantity.
(2) Electric force on a charge in a uniform electric field (E) is constant hence acceleration is constant, so equation of motion can be used (acceleration ) a=qEm
Isolated Charge:
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Electric Field Due to a Point Charge |
E=14πε0Qr2ˆr
Potential, V=14πε0Qr
Potential, V=14πε0Qr
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Variation of Electric Field with Distance |
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Variation of Potential with Distance |
→E∥=14πε02→px3
→E⊥=14πε0→py3
E=14πε0p√3cos2θ+1r3
A Charged Ring:
For a charged ring of radius R
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Field due to Charge Ring |
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Variation of Electric Field along the axis of the Ring |
EP=KQx(R2+x2)32
(1) If x≫R then, Ep=KQx2
(2) If x≪R then, EP=kQxR3
(3) As x increases Electric field →E due to ring first increses then decreases and at x=±R√2 it is maximum.
A Charged Disc:
E=σ2ε0[1−x√x2+R2]
An Infinite sheet of Charge:
E=σ2ε0
Here we noted that, E∝r0 and
Potential V=−σr2ε0+C
Electric Field Due To Two Parallel Plane Sheet of Charged:
Consider two large, uniformly charged parallel plates A and B having surface charge densities are σA and σB respectively. Suppose net electric field at point P, Q and R is to be calculated,
At P, EP=(EA+EB)=12ε0(σA+σB)
At Q, EQ=(EA−EB)=12ε0(σA−σB)
At R, ER=−(EA+EB)=−12ε0(σA+σB)
If, σA=+σ and, σB=−σ then,
EP=ER=0 and EQ=σε0
Thus in case of two infinite plane sheet of charge having equal and opposite surface charge densities, the field in non-zero only in the space between the two sheet and is independent of the distance between them, i.e., field is uniform in this region.
Conducting Sheet of Charge:
E=σε0 and
V=−σrε0+C
An Infinite Long Line of Charge:
E=λ2πε0r
A Finite Line of Charge:
E⊥=λ4πε0x(sinα+sinβ)
E∥=λ4πε0x(cosα−cosβ)
Charged Spherical Shell or Charged Solid Conducting Sphere (Surface Charge Distribution):
(1) Outside the Sphere/Shell:
Here P is a point outside the sphere at a distance r from the centre at which electric field and potential is to be determined.
Electric Field at P,
Eout=14πε0Qr2=σR2ε0r2 and,
Vout=14πε0Qr=σR2ε0r
(2) At The Surface of The Sphere/Shell:
At Surface, r=R
So, ES=14πε0QR2=σε0 and,
VS=14πε0QR=σRε0
(3) Inside of The Shell/Sphere:
Inside the conducting charged sphere, electric field is zero and potential remains constant every where and equal to the potential at the surface.
0<r<R, Ein=0 and Vin=cons.=VS
Solid Non-Conducting Sphere of Charge (Volume Charge Distribution):
Charge given to a non-conducting spheres spreads uniformly throughout its volume.
(1) Outside The Sphere at P:
Eout=14πε0Qr2 and Vout=14πε0Qr
By Using, ρ=Q43πR3 we get,
Eout=ρR33ε0r2 and Vout=ρR33ε0r
(2) At Surface of The Sphere:
At surface, r=R
ES=14πε0QR2=ρR3ε0 and VS=14πε0QR=ρR23ε0
(3) Inside The Sphere:
At a distance r from the centre
Ein=14πε0QrR3=ρr3ε0, Here, Ein∝r and Vin=14πε0Q(3R2−r2)2R3=ρ(3R2−r2)6ε0
(4) At the centre r=0, So Vcentre=32×14πε0QR=32VS
Therefore, Vcentre>Vsurface>Vout
A Charged Disc:
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A disc of Charge |
An Infinite sheet of Charge:
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A Charged Infinite Sheet |
Here we noted that, E∝r0 and
Potential V=−σr2ε0+C
Electric Field Due To Two Parallel Plane Sheet of Charged:
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Two Parallel Plane Charged Sheet |
At P, EP=(EA+EB)=12ε0(σA+σB)
At Q, EQ=(EA−EB)=12ε0(σA−σB)
At R, ER=−(EA+EB)=−12ε0(σA+σB)
If, σA=+σ and, σB=−σ then,
EP=ER=0 and EQ=σε0
Thus in case of two infinite plane sheet of charge having equal and opposite surface charge densities, the field in non-zero only in the space between the two sheet and is independent of the distance between them, i.e., field is uniform in this region.
Conducting Sheet of Charge:
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Conducting Sheet of Charge |
V=−σrε0+C
An Infinite Long Line of Charge:
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An infinite long Charged wire |
A Finite Line of Charge:
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A finite long Charged Wire |
E∥=λ4πε0x(cosα−cosβ)
Charged Spherical Shell or Charged Solid Conducting Sphere (Surface Charge Distribution):
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Solid Charged Conducting Sphere |
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Charged Conducting Shell |
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Variation of Electric Field With Distance |
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Variation of Potential With Distance |
Here P is a point outside the sphere at a distance r from the centre at which electric field and potential is to be determined.
Electric Field at P,
Eout=14πε0Qr2=σR2ε0r2 and,
Vout=14πε0Qr=σR2ε0r
(2) At The Surface of The Sphere/Shell:
At Surface, r=R
So, ES=14πε0QR2=σε0 and,
VS=14πε0QR=σRε0
(3) Inside of The Shell/Sphere:
Inside the conducting charged sphere, electric field is zero and potential remains constant every where and equal to the potential at the surface.
0<r<R, Ein=0 and Vin=cons.=VS
Solid Non-Conducting Sphere of Charge (Volume Charge Distribution):
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Charged Non-Conducting Sphere |
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Variation of Electric Field with Distance |
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Variation of Potential with Distance |
(1) Outside The Sphere at P:
Eout=14πε0Qr2 and Vout=14πε0Qr
By Using, ρ=Q43πR3 we get,
Eout=ρR33ε0r2 and Vout=ρR33ε0r
(2) At Surface of The Sphere:
At surface, r=R
ES=14πε0QR2=ρR3ε0 and VS=14πε0QR=ρR23ε0
(3) Inside The Sphere:
At a distance r from the centre
Ein=14πε0QrR3=ρr3ε0, Here, Ein∝r and Vin=14πε0Q(3R2−r2)2R3=ρ(3R2−r2)6ε0
(4) At the centre r=0, So Vcentre=32×14πε0QR=32VS
Therefore, Vcentre>Vsurface>Vout
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