ElectroStatics - Questions With Answers (Short Notes)
1. State Stokes Theorem.
Answer: The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
∫ H.dl = ∫ ∫ ( ∆ x H ) ds
where, H is the Magnetic field intensity
2. State The Condition For The Vector F To Be Solenoidal.
Answer:
∆ . F = 0
where, F = A i + B i + C i
3. State The Condition For The Vector F To Be Irrotational.
Answer:
∆ x F = 0
where, F = A i + B i + C i4. Give The Relationship Between Potential Gradient and Electric Field.
Answer:
E = - ∆V
5. What Is The Physical Significance Of div D ?
Answer: The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
6. What Are The Sources Of Electric Field & Magnetic Field?
Answer: Stationary charges produce electric field that are constant in time, hence the term electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
7. State Divergence Theorem.
Answer: The integral of the divergence of a vector over a volume v is equal to the surface
integral of the normal component of the vector over the surface bounded by the volume.
∫∫∆.F ds = ∫∫∫ F dv
where, F=A i + B i + C i
8. Define Divergence.
Answer: The divergence of a vector F at any point is defined as the limit of its surface integral
per unit volume as the volume enclosed by the surface around the point shrinks to zero.
9. What Are The Two Important Laws of Electrostatics? State The Basic Difference Between Them.
Answer: The two important laws of electrostatics are
- Coulomb’s Law.
- Gauss’s Law.
Both these laws are used to find the electric field due to charge configurations. Coulomb’s law is applicable in finding electric field due to any charge configurations where as Gauss’s law is applicable only when the charge distribution is symmetrical.
10. State Coulomb's Law.
Answer: Coulomb's Law states that the force (F) between any two point charges (Q1 and Q2) is
directly proportional to the product of their magnitudes and inversely proportional to the square of the distance ® between them. It is directed along the line joining the two charges.
F = (Q1 Q2) / (4Πεr2) dr
Coulomb's law states that “ The force of attraction or repulsion between two point charges Q1 and Q2 is:
- Proportional to the charges Q1 and Q2.
- Varies inversely as the square of distance between them.
- Acts along the line joining the two point charges.
11. State Gauss Law For Electric Fields.
Answer: The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
In Other words, Gauss Law states that the net electric flux emanating or coming from a closed surface S is equal to the total charge contained within the volume V bounded by that surface.
12. Define Electric Flux.
Answer: The lines of electric force is known as electric flux. Electric line of force is a pictorial representation of the electric field.
Electric line of force (also called Electric Flux lines or Streamlines) is an imaginary straight or curved path along which a unit positive charge tends to move in an electric field.
13. State The Properties Of Electric Lines oF Forces.
Answer: Properties of electric lines of forces are:
- Lines of force start from positive charge and terminate either at negative charge or move to infinity.
- Similarly lines of force due to a negative charge are assumed to start at infinity and terminate at the negative charge.
- Lines of force never intersect i.e. they do not cross each other.
- Tangent to a line of force at any point gives the direction of the electric field E at that point.
- Lines are dense close to a source of the electric field and become sparse when one moves away.
- The number of lines per unit area, through a plane at right angles to the lines, is proportional to the magnitude of E. This means that, where the lines of force are close together, E is large and where they are far apart E is small.
14. Define Electric Flux Density.
Answer: Electric flux density is defined as electric flux per unit area. Line of Force may be termed as ‘Electric Flux’ represented by ψ and unit is coulomb (C). The density of electric flux is the electric (displacement) flux density, D.
It is the measure of cluster of ‘electric lines of force’. It is the number of lines of force per unit area of cross section.
D = ψ / S → ψ = ∫S (D . ds)
15.Define Electric Field Intensity.
Answer: Electric field intensity is defined as the electric force per unit positive charge. Also Electric field intensity or the electric field strength at a point is defined as the force per unit charge.
Mathematically,
E = F / Q
or
F = E Q
The force on charge Q is the product of a charge (which is a scalar) and the value of the electric field (which is a vector) at the point where the charge is located.
16. Name Few Applications Of Gauss Law In Electrostatics.
Answer: Gauss law is applied to find the electric field intensity from a closed surface.
Ex: Electric field can be determined for shell, two concentric shell or cylinders etc.
17. State The Relationship Between Electric Field Intensity(E) & Electric Potential(V)?
Answer: Electric field intensity (E) is the negative gradient of Electric potential (V). The negative sign shows that E is directed from higher to lower values of V i.e. E is opposite to the direction in which V increases.
Since Electric potential is a scalar quantity, hence dV (as a function of x, y and z variables) can be written as:
Answer: - An equipotential surface refers to a surface where the potential is constant. The intersection of an equipotential surface and a plane results into a path called an equipotential line.
No work is done in moving a charge from one point to the other along an equipotential line or surface i.e. VA – VB = 0
Hence,
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