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<br><img src="/images/question-image/engineering-physics/electromagnetic-theory/1689581090-two-charges-q-and-2q-are.png" title="Electromagnetic Theory mcq question image" alt="Electromagnetic Theory mcq question image">

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

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

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

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

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

Consider a conducting loop of radius a and total loop resistance R placed in a region with a magnetic field B thereby enclosing a flux $${\phi _0}$$ . The loop is connected to an electronic circuit as shown, the capacitor being initially uncharged.
Electromagnetic Theory mcq question image

If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage V_out is independent of

A

$${\phi _0}$$

B

u

C

R

D

C

A rod of length L with uniform charge density $$\lambda $$ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angularvelocity $$\overrightarrow \omega $$ as shown in the figure below. $$\left( {{\bf{\hat r}},\,\hat \phi ,\,{\bf{\hat z}}} \right)$$ refer to the unit vectors at Q, $$\overrightarrow {\bf{A}} $$ is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and $$\overrightarrow {\bf{J}} $$ is the current density due to the motion of the rod. Which one of the following statements is correct?
Electromagnetic Theory mcq question image

A

$$\overrightarrow {\bf{J}} {\text{ along }}{\bf{\hat r}};\overrightarrow {\bf{A}} {\text{ along }}{\bf{\hat z}};\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{d}$$

B

$$\overrightarrow {\bf{J}} {\text{ along }}\hat \phi ;\overrightarrow {\bf{A}} {\text{ along }}\hat \phi ;\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{{{d^2}}}$$

C

$$\overrightarrow {\bf{J}} {\text{ along }}{\bf{\hat r}};\overrightarrow {\bf{A}} {\text{ along }}{\bf{\hat z}};\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{{{d^2}}}$$

D

$$\overrightarrow {\bf{J}} {\text{ along }}\hat \phi ;\overrightarrow {\bf{A}} {\text{ along }}\hat \phi ;\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{d}$$

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