At the interface between two linear dielectrics (with dielectric constants $${{\varepsilon _1}}$$ and $${{\varepsilon _2}}$$), the electric field lines bend, as shown in the figure. Assume that there are no free charges at the interface. The ratio $$\frac{{{\varepsilon _1}}}{{{\varepsilon _2}}}$$ is<br><img src="/images/question-image/engineering-physics/electromagnetic-theory/1689579344-at-the-interface-between-two-linear-dielectrics.png" title="Electromagnetic Theory mcq question image" alt="Electromagnetic Theory mcq question image">

Two dielectric materials A and B exhibit both ionic and orientational polarizabilities. The variation of their susceptibilities $$\chi \left( { = {\varepsilon _r} - 1} \right)$$ with temperature T is shown in the figure, where $${\varepsilon _r}$$ is the relative dielectric constant. It can be inferred from the figure that
Solid State Physics mcq question image

A

A is more polar and it has a smaller value of ionic polarizability than that of B

B

A is more polar and it has a higher value of ionic polarizability than that of B

C

B is more polar and it has a higher value of ionic polarizability than that of A

D

B is more polar and it has a smaller value of ionic polarizability than that of A

Four charges are placed at the four corners of a square of side a as shown in the figure. The electric dipole moment of this configuration is
Electromagnetic Theory mcq question image

Electromagnetic Theory mcq question image

A

$$\overrightarrow {\bf{p}} = qa{\bf{\hat i}} + qa{\bf{\hat j}}$$

B

$$\overrightarrow {\bf{p}} = - qa{\bf{\hat i}} + qa{\bf{\hat j}}$$

C

$$\overrightarrow {\bf{p}} = - qa{\bf{\hat i}} - qa{\bf{\hat j}}$$

D

$$\overrightarrow {\bf{p}} = qa{\bf{\hat i}} - qa{\bf{\hat j}}$$

Two charges q and 2q are placed along the X-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and 1.5 m from the plane. The force acting on the charge q is
Electromagnetic Theory mcq question image

A

$$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{7{q^2}}}{2}$$

B

$$\frac{1}{{4\pi {\varepsilon _0}}}2{q^2}$$

C

$$\frac{1}{{4\pi {\varepsilon _0}}}{q^2}$$

D

$$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q^2}}}{2}$$

Choose the correct statements regarding dielectric. (i) Dielectrics have free electrons (ii) Dielectric does not have free electrons (iii) Dielectrics are conductor

A

Only (ii) is true

B

Only (ii) and (iii) are true

C

Only (i) and (iii) are true

D

Only (iii) are true

Four point charges are placed at the corners of a square whose centre is at the origin of a Cartesian coordinate system. A point dipole $$\overrightarrow {\bf{p}} $$ is placed at the centre of the square as shown in the figure. Then,
Electromagnetic Theory mcq question image

A

there is no force acting on the dipole

B

there is no torque about the centre at O on the dipole

C

the dipole has minimum energy if it is in $${{{\bf{\hat e}}}_x}$$ direction

D

the force on the dipole is increased if the medium is replaced by another medium with larger dielectric constant

A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the Z-direction with one end at the origin as shown below.
Electromagnetic Theory mcq question image

If the rod carries a polarization $$\overrightarrow {\bf{P}} = \left( {5{z^2} + 7} \right){\bf{\hat k}},$$ the volume bound charge inside the dielectric is

A

zero

B

10πr²L

C

-5πr²L

D

-5πr²L²

Consider a set of two stationary point charges q₁ and q₂ as shown in the figure. Which of the following statements is correct?
Electromagnetic Theory mcq question image

A

The electric field at P is independent of q₂

B

The electric flux crossing the closed surface S is independent of q₂

C

The line integral of the electric field $$\overrightarrow {\bf{E}} $$ over the closed contour C depends on q₁ and q₂

D

$$\overrightarrow \nabla .\overrightarrow {\bf{E}} = 0$$ everywhere

The Coordinator of an International Virtual Conference has planned six guest lectures on different areas-Cryptography, Fluid Dynamics, Big Data Analysis, Wavelet Theory, Differential Equations and Linear Algebra-to be organised only one on each day from Monday to Sunday. Wavelet Theory should be organised immediately after Differential Equations. Big Data Analysis should be organised on Wednesday and should not be followed by Linear Algebra. Fluid Dynamics should be organised on Friday and there should be a gap of two days between Cryptography and Linear Algebra. One day there will be no lecture (Saturday is not that day), and just before that day Linear Algebra will be organised. How many lectures are organised between Big Data Analysis and Wavelet Theory?

A

Two

B

One

C

Four

D

Three

A dielectric and a conductor are placed in an external electric field of magnitude Eext. The charge density induced at the surface of the dielectric and the conductor are σd and σe respectively. The net electric field inside the dielectric and the conductor are Ed and Ec respectively. Then,

A

σd = σe

B

σd > σe

C

Ed = Ec = Eext

D

Ed > Ec

The figure shows a shape ABC and its mirror image A₁B₁C₁ across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A₁B₁C₁ is
Linear Algebra mcq question image

A

\\

B

\\

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