Chapter Questions
What is the characteristic of a vector in a vector field?
What is the characteristic of a scalar in a scalar field?
What is a line integral? Give a few physical examples of line integrals.
What is circulation of a vector field?
What is a surface integral? Give a few physical examples of surface integrals.
What is the gradient of a scalar function? What is its direction?
What is a lamellar vector field? What is a non-lamellar vector field?
What is the physical significance of divergence of a vector function?
What is flux of a vector function?
Define gradient of a scalar function in terms of integrals.
Define divergence of a vector function. Is the resultant a vector or a scalar?
Define irrotational vector field. Give examples.
Which theorem transforms surface integrals to volume integrals? State it.
State Gauss's law in the electrostatic field in integral form.
Write down Gauss's law in the gravitational field of a body.
How do you define magnetic flux linked with a surface in case of non-uniform magnetic field?
Write down the conditions for the validity of Ampere's circuital law.
Derive the relation between displacement current and electric displacement.
State Maxwell's electromagnetic equation, which is a consequence of Gauss's law in electrostatics.
Explain why the electric field due to static charges is a lamellar vector field.
Evaluate the gradient of the magnitude of a position vector. [Ans. Unit vector]
What is the physical significance of a gradient of a scalar function?
Define divergence of a vector function in terms of integrals.
Define curl of a vector function. Is the resultant a vector or a scalar?
What is the physical significance of curl of a vector function?
Define curl of a vector function in terms of integrals.
How can you get a scalar function from a vector field and how can you get a vector function from a scalar field? Give physical examples of both the cases.
Define solenoidal vector field. Give examples.
Define conservative vector field. Give examples.
Define rotational vector field. Give examples.
Define non-conservative vector field. Give examples.
Which theorem transforms line integrals to surface integrals? State it.
State Green's theorem in a plane.
Evaluate the divergence of a position vector.
Evaluate the gradient of a position vector.
What is the gradient of a scalar function in terms of rectangular coordinates?
What is the divergence of a vector function in terms of rectangular coordinates?
What is the curl of a vector function in terms of rectangular coordinates?
Define electric field intensity in terms of electric flux.
Can you define electric field intensity in terms of electric potential?
What are polar and non-polar molecules of a dielectric? Give some examples.
What do you mean by electric displacement?
Distinguish between electric field intensity vector and electric displacement vector.
With what charges are electric field intensity vector, electric displacement vector and electric polarization vector related to?
What is the inherent meaning of Gauss's law?
What is a Gaussian surface?
Transform Gauss's law in electrostatic field in the integral form into its corresponding differential form.
State Gauss's law in electrostatic field in differential form.
State Gauss's law in magnetic field in differential form.
State Gauss's law in magnetic field in integral form.
Use Gauss's divergence theorem to transform the integral form of Gauss's law in magnetic field into its differential form.
State Gauss's law in electrostatic field in the integral form for a dielectric medium.
State Gauss's law in electrostatic field in differential form for a dielectric medium.
Using Gauss's law, calculate the field intensity due to a point charge.
Using Gauss's law, calculate the field intensity due a spherically symmetric charge distribution of uniform density when the point lies inside the charge distribution.
Using Gauss's law, calculate the field intensity due a spherically symmetric charge distribution of uniform density when the point lies outside the charge distribution.
Using Gauss's law, calculate the field intensity due a spherically symmetric charge distribution of uniform density when the point lies on the surface of the charge distribution.
Using Gauss's law, calculate the field intensity due a cylindrically symmetric charge distribution of uniform density of infinite length when the point lies inside the charge distribution.
Using Gauss's law, calculate the field intensity due a cylindrically symmetric charge distribution of uniform density of infinite length when the point lies outside the charge distribution.
Using Gauss's law, calculate the field intensity due a cylindrically symmetric charge distribution of uniform density of infinite length when point lies on the surface of the charge distribution.
Using Gauss's law, calculate the field intensity due a linear distribution of charge of infinite length.
Plot the variation of electric field intensities in case of a cylindrically symmetric charge distribution of charge of uniform density.
Using Gauss's law, calculate the field intensity at nearby points of both sides of a uniformly charged non-conducting sheet of infinite extension.
Using Gauss's law, calculate the field intensity at a nearby point over a uniformly charged conducting body of infinite extension.
What will be Gauss's law for magnetic field?
Prove Coulomb's law in electrostatics from Gauss's law.
A certain region of space bounded by an imaginary closed surface (Gaussian surface) contains no charge. Is the electric field intensity always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?
Would Gauss's law hold true if the exponent in Coulomb's law were not exactly 2?
Would Gauss's law hold true if the surface area of a sphere is not $4 \pi \mathrm{r}^2$ ?
Plot the variation of electric field intensities with respect to radial distance in case of a spherically symmetric charge distribution of uniform density.
What is magnetic induction? What are its units?
What are the dimensions of magnetic induction in the SI system?
What is magnetic field intensity vector? What are its units?
What are the dimensions of the magnetic intensity vector in SI system?
is there any relation between magnetic induction vector and magnetic intensity vector? If yes, write it for different media.
What is Maxwell's corkscrew rule? Explain it.
What is the right-hand rule for finding the direction of magnetic induction near a wire carrying current?
What is the effect of magnetic field on a moving charge?
Discuss the motion of a charge under the combined effects of electric and magnetic fields.
Is magnetic induction constant for points that lie on a given line of induction? Explain.
Current is flowing from down to up in a vertical wire. Depict the direction of the magnetic induction and magnetic intensity at different points on a fixed horizontal plane.
What is the inherent meaning of Ampere's circuital law?
Write down Ampere's circuital law in integral and differential form due to a current carrying wire.
Compare Gauss's law and Ampere's circuital law.
A certain closed path encloses no electric current. Is the magnetic induction always zero everywhere on the closed path? If not, under what circumstances is it zero on the path?
Would Ampere's law hold true if the exponent in Biot-Savart's law were not exactly 2?
Would Ampere's law hold true if the perimeter of a circular path is not $2 \pi$ ?
In a current carrying circular loop of wire is the magnetic induction uniform for all the points inside the loop?
Using Ampere's circuital law, calculate the magnetic induction at a nearby point due to a current carrying wire of infinite extension.
Using Ampere's circuital law, calculate the magnetic induction due a cylindrical current carrying conductor of infinite length when the point lies inside the conductor.
Using Ampere's circuital law, calculate the magnetic induction due a cylindrical current carrying conductor of infinite length when the point lies outside the conductor.
Using Ampere's circuital law, calculate the magnetic induction due a cylindrical current carrying conductor of infinite length when the point lies on the surface of the conductor.
Plot the variation of magnetic induction in case of a cylindrical current carrying conductor with respect to radial distance.
What is displacement current?
How can displacement current be produced? Explain.
Why is the quantity $\varepsilon_O \frac{d \varphi_E}{d t}$ referred to as (displacement) current?
State and prove the relation between displacement current density and electric displacement.
What are the different ways of setting up of magnetic fields?
Generalize Ampere's circuital law taking into consideration the conduction current, magnetizing current and displacement current.
State Faraday's law of electromagnetic induction.
State Lenz's law.
Is induced electric field conservative or non-conservative?
Is static electric field conservative or non-conservative?
Compare static electric field and induced electric field.
Can induced magnetic field like induced electric field be produced? If yes explain how?
Can electric field for which $\vec{\nabla} \times E \neq 0$ be produced? If yes how can it be produced?
State Faraday's law of electromagnetic induction in integral form.
State Faraday's law of electromagnetic induction in differential form.
What does equation of continuity in electromagnetism represent?
State Maxwell's electromagnetic equations in differential form.
State Maxwell's electromagnetic equations in integral form.
State Maxwell's electromagnetic equations in free space/vacuum.
State Maxwell's electromagnetic equations in a medium containing charges and currents.
State Maxwell's electromagnetic equations in a medium containing no charges and currents.
State Maxwell's electromagnetic equations in a linear and isotropic medium containing charges and currents.
State Maxwell's electromagnetic equations in a linear and isotropicmedium containing no charges and currents.
Write the Maxwell's electromagnetic equations, which are not changed due to the presence of currents and charges.
Write Maxwell's electromagnetic equations, which are changed due to the presence of currents and charges.
State Maxwell's electromagnetic equation which follows from the generalized Ampere's circuital law.
State Maxwell's equation which supports the concept of non-existence of magnetic monopole.
State Maxwell's electromagnetic equation which is a consequence of Faraday's law of electromagnetic induction.
Write down Maxwell's electromagnetic equations for a harmonically varying field defined by $\vec{D}=\vec{D}_0 e^{\text {iott }}$ and $\vec{B}=\vec{B}_0 e^{\text {ist }}$.