Electrostatics Flashcards
What factors do tubes of force originating from a charge depend on?
Magnitude of charge
Permitivity of medium surrounding the charge
Define Electric tubes of force.
Electric lines of force from a small surface area of positively charged conductor encloses a tube like structure and are called electric tubes of force.
Define TNEI
Total number of tubes of induction passing normally through a given surface area is known as the total normal electric induction.
Define NEI
Number of tubes of induction passing normally through a unit area drawn round a uniform electric field is called Normal Electric Induction.
State Gauss’ theorem
According to Gauss’ theorem, the TNEI over any surface is equal to the sum of charges enclosed by that surface.
Electrical intensity at a point outside a charged conducting sphere- derivation.
Gaussian sphere of radius r.
E= (1/4πε)* (q/r2)
= ( RRσ/(εrr))
Electric field intensity at a Point outside infinitely infinitely long charged conducting cylinder - derivation
Construct Gaussian cylinder
E = (1/2πε)*(q/r)
q= charge per unit length
Electric field intensity at a point outside and near surface of charged conductor of any shape- derivation
Construct small cylinder
Equate , no integration
E= σ/ε
Electric field intensity due to uniformly charged infinite plane sheet- derivation
Construct an imaginary cylinder around P with axis perpendicular to plane sheet and ends having area of cross section ds.
Equate, no integration
E= σ/(2*ε)
Electric field intensity due to uniformly charged infinite plane sheet - Expression
E= σ/(2*ε)
Electric field intensity at a point outside and near surface of charged conductor of any shape- expression
E= σ/ε
Electric field intensity at a Point outside infinitely infinitely long charged conducting cylinder - expression
E = (1/2πε)*(q/r) q= charge per unit length
Electrical intensity at a point outside a charged conducting sphere- expression
E= (1/4πε)* (q/r2)
= ( RRσ/(εrr))
Derivation for mechanical force acting per unit area on the surface of a charged conductor.
E1=E2=(σ/(2*ε))
Mechanical force= charge on ds * electric intensity due to charge of remaining area of conductor
f= F/ds = σσ/(2ε) = (1/2)εE*E
What is the direction of mechanical force per unit area?
Always directed outwards (σ*σ always positive)
Define energy density
The electrostatic energy per unit volume is called energy density.
Derivation for energy density of a medium
dW=F.dl
du/dv = (1/2)εE*E
Define dielectrics
Dielectrics are non-conducting substances with no free charges or electrons.
Define Polar molecule
A polar molecule is a molecule in which “centre of gravity” of positive nucleus and revolving electrons do not coincide.
Define non-polar molecule
A non-polar molecule is a molecule in which “centre of gravity” of positive nucleus and revolving electrons coincide.
Define Polarisation (electrostatics)
Polarisation is defined as dipole moment per unit volume.
Or
Polarisation may be defined at amount of induced surface charge per unit area or the surface density of Polarisation charges appearing at right angles to external electric field.
Give and expression for Polarisation
P= χe*E
χe—> electric susceptibility of dielectric material
Or
P= (Polarization charges (qp) / area of cross section of dielectrics) - charge density of Polarisation charges (σ p)
Linear isotropic substances
Linear isotropic substances are substances in which induced dipole moment is induced in the di erection of field and proportional to field strength.
How do polarized dielectrics work?
A polarized dielectric is equivalent to two charged surfaces with induced charges (polarization charges). These induced surface charges oppose the external electric field and so weaken the original field within the dielectric.
Define capacitor
Capacitor is a system of conductors having equal and opposite charges separated by an insulator (insulating medium) or dielectric.
Define capacitance of a capacitor
The capacitance of a capacitor is defined as the ratio of magnitude of charge on either of the conductors to the magnitude of potential difference between two conductors.
Give the expression for capacitance of a capacitor
C= Q/V
What is capacitance?
The ability of a conductor to store electric charge and electric potential energy is known as capacitance of the capacitor.
Why is condenser a misnomer?
Capacitor doesn’t condense energy but stores it.
Applications of capacitor
Tuning of radio circuit.
Smoothing rectified current in power suppliers.
Elimination of sparking points when they are open or close in and ignition system of automobile engine.
Storage of large amount of charge for use in nuclear reactors.
Define the SI unit of capacitance
A capacitor is said to have a capacitance of one farad if the potential difference across it rises by one volt when one coulomb of charge is given to it.
Explain the concept of a parallel plate capacitor
Voltage decreases, capacity increases when p2 bought near p1
What are the types of capacitors? Draw diagrams.
Parallel plate capacitor
Cylindrical capacitor
Spherical capacitor
199
Capacitance of a parallel plate capacitor - derivation
Pg 199-200 E= σ/ε E= Q/(A*ε) E= V/d Equate C= A*ε / d
Capacitance of a parallel plate capacitor - expression
C= A*ε/ d
What does the capacity of a parallel plate condenser depend on?
Directly : area of plates , dielectric constant of medium
Inversely : distance of separation between the two plates
Define dielectric constant (with ref. to capacitor)
Dielectric constant is the factor by which the capacitance increases from its value in air when the dielectric material is fully inserted between the two plates of the parallel plate condenser.
Explain the effect of dielectrics on capacity
Cd= k* Cair
Surface charge on conducting plate does not change but induced charge of opposite sign appears on each surface of dielectric.
Pg 200
Cd=Co(Eo/Ed)
Capacitance of a capacitor is increased in proportion to the ratio of electric field without dielectric and with dielectric in the space between the plates of capacitor.
Energy of a charged capacitor - derivation
v=q/c (at intermediate stage during process if charging)
dW= v.dq
Integrate
W= QQ / 2C = (1/2)CVV = (1/2)QV
Energy of a charged capacitor - expression
W= QQ / 2C = (1/2)CVV = (1/2)QV
When are capacitors said to be connected in series?
Capacitors are said to be connected in series if they are connected one after another in the form of a chain.
Derive a relation for capacitors connected in series
V= V1+ ….. +Vn
Q constant
1/Cs = (1/C1) + …… + (1/Cn)
When are capacitors said to be connected in parallel?
If capacitors are connected between two common points or junctions, they are said to be connected in parallel.
Derive a relation for capacitors connected in parallel.
Q= Q1 + …… + Qn
V constant
Cp= C1 + …… + Cn
Define Artificial Transmutation
Artificial transmutation is the process in which bombardment of highly energetic particles on nucleus of and element causes it to be transformed into some other element.
What is a Van de Graaff generator?
It is a electrostatic generator that can produce high potential of the order of millions of volts and is used to accelerate charged particles such as protons, deuterons, alpha-particles which are then further used for artificial transmutation.
Draw a diagram of Van de Graaff generator. Explain construction and working.
Pg 203 - 204
Why is a Van de Graaff generator enclosed in and Earth connected steel tank filled with air under pressure?
The potential dome continuously increases due to accumulation of positive charges. Charges are crowded on outer surface of dome which leaks to the surroundings in the form of a spark. Two avoid such a leakage, Van de Graaff generator is enclosed in an earth connected steel tank filled with air under pressure.
Uses of Van de Graaff generator
Produce High potential of the order of few million volts
Accelerate charged particles such as protons, deuterons, alpha-particles.
Used in nuclear physics for study involving collision experiments for probing nuclear structure, producing different radioactive elements / isotopes for carrying out nuclear reactions, nuclear disintegration.
In medicine such beams are used to treat cancer.
