Two magnetic dipoles of magnitude m each are placed in a plane as shown below. The energy of interaction is given by<br><img src="/images/question-image/engineering-physics/electromagnetic-theory/1689419840-two-magnetic-dipoles-of-magnitude-m-each.png" title="Electromagnetic Theory mcq question image" alt="Electromagnetic Theory mcq question image">

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

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

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

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

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 circular arc QTS is kept in an external magnetic field $${\overrightarrow {\bf{B}} _0}$$ as shown in figure. The arc carries a current $$l$$. The magnetic field is directed normal and into the page. The force acting on the arc is
Electromagnetic Theory mcq question image

A

$$2l{B_0}R{\bf{\hat k}}$$

B

$$l{B_0}R{\bf{\hat k}}$$

C

$$ - 2l{B_0}R{\bf{\hat k}}$$

D

$$ - l{B_0}R{\bf{\hat k}}$$

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

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

Five boxes B1, B2, B3, B4 and B5 are placed one above the other in racks. The lowermost rack is numbered as one and just above the lowermost is numbered as two and so on. Each box is coloured with different colour such as L1, L2, L3, L4 and L5 (not necessarily in the same order). Two boxes are placed between L2 coloured box and L5 coloured box. Box B1 is not placed immediately above box B3. Box B4 is placed in the top most rack. L1 coloured box is placed immediate above L5 coloured box. Box B3 is coloured with L4. L5 coloured box is placed above L4 coloured box. Box B2 is coloured with L1. Which of the following boxes are placed immediately above and immediately below B5 box respectively?

A

B4 and B1

B

B3 and B2

C

B2 and B3

D

B1 and B3

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

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

Which of the following statements are true for renewable energy? a. Energy obtained from natural and persistent flow of energy occurring in the immediate environment. b. The renewable energy is obtained from static stores of energy that remain underground unless released by human interaction. c. It is also called as Green energy Sustainable energy. d. It is the energy supplied by finite supplies or Brown energy.

A

a and b

B

b and c

C

a and c

D

c and d

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer. There are six letters E, I, P, G, N and O is PIGEON the word formed after performing the following operations using these six letters only? I. O is placed fourth to the right of P. G is not placed immediately next to either P or O. II. N is placed immediately next (either left or right) to O. E is placed immediately next (either left or right) to G. III. Both I and E are placed immediately next to G. The word does not begin with N. P is not placed immediately next to E.

A

If the data in statement I and II are sufficient to answer the question, while the data in statement III alone are not sufficient to answer the question.

B

If the data in statement I and III are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

C

If the data in statement II and III are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

D

If the data either statement I alone or statement II alone or statement III alone are sufficient to answer the question.

Two magnetic dipoles of magnitude m each are placed in a plane as shown below. The energy of interaction is given by

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