Electromagnetic Theory MCQs Question and Answer in Engineering Physics Page-3 section-1

21.
If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$ (x² + y² + z²), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be

A. zero

B. $$ - 6\,{\phi _0}{\varepsilon _0}$$

C. $$ - 2\,{\phi _0}{\varepsilon _0}$$

D. $$ - \frac{{6\,{\phi _0}}}{{{\varepsilon _0}}}$$

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22.
Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct?
(where, r is the radial distance from the axis of the cylinder)

A. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{everywhere}}} \right)$$

B. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{everywhere}}} \right)$$

C. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{for }}r > R} \right)$$

D. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{for }}r > R} \right)$$

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23.
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

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

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24.
The trace of a 3 × 3 matrix is 2. Two of its eigen values are 1 and 2. The third eigen value is

A. -1

B. 0

C. 1

D. 2

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25.
An infinite conducting sheet in the X-Y-plane carries a surface current density K along the Y-axis. The magnetic field $$\overrightarrow {\bf{B}} $$ for z > 0 is

A. $$\overrightarrow {\bf{B}} = 0$$

B. $$\overrightarrow {\bf{B}} = {\mu _0}K\overrightarrow {\bf{k}} /z$$

C. $$\overrightarrow {\bf{B}} = {\mu _0}K\overrightarrow {\bf{i}} /2$$

D. $$\overrightarrow {\bf{B}} = {\mu _0}K\overrightarrow {\bf{j}} /{\left( {{x^2} + {z^2}} \right)^{0.5}}$$

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26.
A plane electromagnetic wave of frequency ω is incident normally on an air-dielectric interface. The dielectric is linear, isotropic, non-magnetic and its refractive index is n. The reflectance (R) and transmittance (T) from the interface are

A. $$R = {\left( {\frac{{n - 1}}{{n + 1}}} \right)^2},\,T = \frac{{4n}}{{{{\left( {n + 1} \right)}^2}}}$$

B. $$R = - \left( {\frac{{n - 1}}{{n + 1}}} \right),\,T = \frac{2}{{{{\left( {n + 1} \right)}^2}}}$$

C. $$R = {\left( {\frac{{n - 1}}{{n + 1}}} \right)^3},\,T = \frac{{4{n^3}}}{{{{\left( {n + 1} \right)}^3}}}$$

D. $$R = \frac{{{{\left( {n - 1} \right)}^2}}}{{n + 1}},\,T = \frac{{4{n^2}}}{{{{\left( {n + 1} \right)}^2}}}$$

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27.
A conducting sphere of radius R has charge +Q on its surface. If the charge on the sphere is doubled and its radius is halved, the energy associated with the electric field will

A. increase four times

B. increase eight times

C. remain the same

D. decrease four times

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28.
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

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

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29.
Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

A. always independent of frequency

B. monotonically decreasing with frequency

C. monotonically increasing with frequency

D. a non-monotonic function of frequency

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30.
A circular disc of radius a on the XY-plane has a surface charge density $$\sigma = \frac{{{\sigma _0}r\cos \theta }}{a}.$$ The electric dipole moment of this charge distribution is

A. $$\frac{{{\sigma _0}\pi {a^4}}}{4}{\bf{\hat x}}$$

B. $$\frac{{{\sigma _0}\pi {a^3}}}{4}{\bf{\hat x}}$$

C. $$ - \frac{{{\sigma _0}\pi {a^3}}}{4}{\bf{\hat x}}$$

D. $$ - \frac{{{\sigma _0}\pi {a^4}}}{4}{\bf{\hat x}}$$

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Electromagnetic Theory MCQs Question and Answer in Engineering Physics

21. If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$ (x2 + y2 + z2), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be

Answer & Solution

22. Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct? (where, r is the radial distance from the axis of the cylinder)

Answer & Solution

23. 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

Answer & Solution

24. The trace of a 3 × 3 matrix is 2. Two of its eigen values are 1 and 2. The third eigen value is

Answer & Solution

25. An infinite conducting sheet in the X-Y-plane carries a surface current density K along the Y-axis. The magnetic field $$\overrightarrow {\bf{B}} $$ for z > 0 is

Answer & Solution

26. A plane electromagnetic wave of frequency ω is incident normally on an air-dielectric interface. The dielectric is linear, isotropic, non-magnetic and its refractive index is n. The reflectance (R) and transmittance (T) from the interface are

Answer & Solution

27. A conducting sphere of radius R has charge +Q on its surface. If the charge on the sphere is doubled and its radius is halved, the energy associated with the electric field will

Answer & Solution

28. 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

Answer & Solution

29. Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

Answer & Solution

30. A circular disc of radius a on the XY-plane has a surface charge density $$\sigma = \frac{{{\sigma _0}r\cos \theta }}{a}.$$ The electric dipole moment of this charge distribution is

Answer & Solution

21.
If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$ (x² + y² + z²), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be

22.
Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct?
(where, r is the radial distance from the axis of the cylinder)

23.
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

24.
The trace of a 3 × 3 matrix is 2. Two of its eigen values are 1 and 2. The third eigen value is

25.
An infinite conducting sheet in the X-Y-plane carries a surface current density K along the Y-axis. The magnetic field $$\overrightarrow {\bf{B}} $$ for z > 0 is

26.
A plane electromagnetic wave of frequency ω is incident normally on an air-dielectric interface. The dielectric is linear, isotropic, non-magnetic and its refractive index is n. The reflectance (R) and transmittance (T) from the interface are

27.
A conducting sphere of radius R has charge +Q on its surface. If the charge on the sphere is doubled and its radius is halved, the energy associated with the electric field will

28.
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

29.
Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

30.
A circular disc of radius a on the XY-plane has a surface charge density $$\sigma = \frac{{{\sigma _0}r\cos \theta }}{a}.$$ The electric dipole moment of this charge distribution is