Electromagnetic Theory

The divergence of the vector field is

The unit of electric field intensity

In Gauss's Law the electric field is related to

The electric field at a point due to an infinite sheet of charge is:

The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and magnetic field is:

The energy density in magnetic field is given by

The dot product of the vectors $ 3i-2j+5k $ and $ -i+3j+2k $ is,

The Pointing vector P is

The Maxwell's equation $ \nabla \cdot B = 0 $ is due to

Curl of gradient of a vector is

Write the differential elements (dl, da, dv) in both Cartesian, cylindrical co-ordinate system.

State divergence theorem. What will be divergence to position vector?

Given the two points, $ C(-3,2,1) $ and $ D(r=5, \theta=20^{\circ}, \varphi=-70^{\circ}) $. find: (i) The spherical coordinates of C (ii) The Cartesian coordinates of D

Find the divergence of $ \vec{A} = 3x^{2}a_{x} + 5x^{2}y^{2}a_{y} + xyz^{3}a_{z} $ where $ a_{x}, a_{y} $ and $ a_{z} $ are unit vectors in cartesian coordinates at point (1,1,1)

State and derive Coulomb's law. Write coulomb's law in vector forms.

Derive an expression for intensity of electric field at a point distant r from a point charge.

An infinite long line charge of uniform density $ \rho_{L} $ C/cm is situated along the z-axis. Obtain electric field intensity due to this charge using Gauss's law.

Derive energy density in electrostatic field.

Four 3pC charges are at the corners of a 1-m square. The two charges at the left side of the square are positive. The two charges on the right side are negative. Find the field E at the centre of the square, $ \epsilon_{r}=1 $

What do you understand by capacitance of a capacitor? Deduce and expression for the capacitance of a parallel plate capacitor. How will it be modified when the gaps between the plates is filled with a dielectric?

Show that the Faraday's law of electromagnetic induction can be expressed as $ \nabla \times E = -\partial B/\partial t $. Write down its integral form.

Explain the concept of displacement current and show how it led to the modification of the Ampere's law.

Discuss reflection of plane electromagnetic wave incident normally on a perfect dielectric and obtain expressions for the two reflection coefficients of electric and magnetic fields.

Define Poynting vector. Mention any two properties of uniform plane wave.

The divergence of the vector field is

The unit of electric field intensity

In Gauss's Law the electric field is related to

The electric field at a point due to an infinite sheet of charge is:

The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and magnetic field is:

The energy density in magnetic field is given by

The dot product of the vectors $3i-2j+5k$ and $-i+3j+2k$ is,

The Pointing vector P is

The Maxwell's equation $\nabla \cdot B = 0$ is due to

Curl of gradient of a vector is

Write the differential elements (dl, da, dv) in both Cartesian, cylindrical co-ordinate system.

State divergence theorem. What will be divergence to position vector?

Given the two points, $C(-3,2,1)$ and $ D(r=5, \theta=20^{\circ}, \varphi=-70^{\circ}) $. find: (i) The spherical coordinates of C (ii) The Cartesian coordinates of D

Find the divergence of $\vec{A} = 3x^{2}a_{x} + 5x^{2}y^{2}a_{y} + xyz^{3}a_{z}$ where $ a_{x}, a_{y} $and$ a_{z} $ are unit vectors in cartesian coordinates at point (1,1,1)

State and derive Coulomb's law. Write coulomb's law in vector forms.

Derive an expression for intensity of electric field at a point distant r from a point charge.

An infinite long line charge of uniform density $\rho_{L}$ C/cm is situated along the z-axis. Obtain electric field intensity due to this charge using Gauss's law.

Derive energy density in electrostatic field.

Four 3pC charges are at the corners of a 1-m square. The two charges at the left side of the square are positive. The two charges on the right side are negative. Find the field E at the centre of the square, $\epsilon_{r}=1$

What do you understand by capacitance of a capacitor? Deduce and expression for the capacitance of a parallel plate capacitor. How will it be modified when the gaps between the plates is filled with a dielectric?

Show that the Faraday's law of electromagnetic induction can be expressed as $ \nabla \times E = -\partial B/\partial t $. Write down its integral form.

Explain the concept of displacement current and show how it led to the modification of the Ampere's law.

Discuss reflection of plane electromagnetic wave incident normally on a perfect dielectric and obtain expressions for the two reflection coefficients of electric and magnetic fields.

Define Poynting vector. Mention any two properties of uniform plane wave.

• Biot-Savart's Law
• Magnetic field boundary condition for isotropic medium
• Skin Effect
• Spherical capacitance

What is physical significance of divergence?

State Stoke's theorem.

How is the unit vectors defined in three co ordinate systems?

State Gauss law for electric fields.

Define dielectric strength.

State Biot-Savarts law.

What is magnetic susceptibility?

Write down the wave equation for E and H in free space.

State Poynting Theorem.

Define intrinsic impedance or characteristic impedance.

Derive the expression for the attenuation constant, phase constant and intrinsic impedance for a uniform plane wave in a good conductor.

Calculate the depth of penetration in copper at 10 MHZ. Given the conductivity of copper is $ 5.8 \times 10^{7} S/m $ and its permeability $ 1.3 mH/m $.

Derive suitable relations for integral and point forms of poynting theorem.

Discuss about the plane waves in lossless dielectrics.

With explanation, derive the Maxwell's equation in differential and integral forms.

An iron ring with a cross sectional area of 3 $ cm^{2} $ and mean circumference of 15 cm is wound with 250 turns wire carrying a current of 0.3A. The relative permeability of ring is 1500. Calculate the flux established in the ring.

Derive the expressions for boundary conditions in magnetic fields.

State and proof gauss law and explain applications of Gauss law.

Explain Poisson's and Lapace's equations.

State and proof divergence theorem.

Define divergence, gradient, curl in spherical co-ordinate system with mathematical expression

Define and explain Biot-Savart Law.

Derive General field relation for time varying electric and magnetic fields using Maxwell's equations.

What is physical significance of divergence?

State Stoke's theorem.

How is the unit vectors defined in three co ordinate systems?

State Gauss law for electric fields.

Define dielectric strength.

State Biot-Savarts law.

What is magnetic susceptibility?

Write down the wave equation for E and H in free space.

State Poynting Theorem.

Define intrinsic impedance or characteristic impedance.

Derive the expression for the attenuation constant, phase constant and intrinsic impedance for a uniform plane wave in a good conductor.

Calculate the depth of penetration in copper at 10 MHZ. Given the conductivity of copper is $ 5.8 \times 10^{7} S/m $and its permeability$ 1.3 mH/m $.

Derive suitable relations for integral and point forms of poynting theorem.

Discuss about the plane waves in lossless dielectrics.

With explanation, derive the Maxwell's equation in differential and integral forms.

An iron ring with a cross sectional area of 3 $cm^{2}$ and mean circumference of 15 cm is wound with 250 turns wire carrying a current of 0.3A. The relative permeability of ring is 1500. Calculate the flux established in the ring.

Derive the expressions for boundary conditions in magnetic fields.

State and proof gauss law and explain applications of Gauss law.

Explain Poisson's and Lapace's equations.

State and proof divergence theorem.

Define divergence, gradient, curl in spherical co-ordinate system with mathematical expression

Define and explain Biot-Savart Law.

Derive General field relation for time varying electric and magnetic fields using Maxwell's equations.

• Equipotential Surface.
• Magnetic Vector potential.
• UHF Transmission line.
• Smith Chart.