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.<br><img src="/images/question-image/engineering-physics/electromagnetic-theory/1689418510-consider-a-conducting-loop-of-radius.png" title="Electromagnetic Theory mcq question image" alt="Electromagnetic Theory mcq question image"><br>If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage V<sub>out</sub> is independent of

Aspherical conductor of radius a is placed in a uniform electric field $$\overrightarrow {\bf{E}} = {E_0}\,{\bf{\hat k}}.$$ The potential at a point P(r, θ) for r > a, is given by $$\phi \left( {r,\,\theta } \right) = {\text{constant}} - {E_0}r\cos \theta + \frac{{{E_0}{a^3}}}{{{r^2}}}\cos \theta $$
where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.

The charge density on the sphere at θ = 30° is

$$3\sqrt 3 {\varepsilon _0}\,{E_0}/2$$

$$3{\varepsilon _0}\,{E_0}/2$$

$$\sqrt 3 {\varepsilon _0}\,{E_0}/2$$

$${\varepsilon _0}\,{E_0}/2$$

The figure shows a constant current source charging a capacitor that is initially uncharged.

If the switch is closed at t = 0, which of the following plots depicts correctly the output voltage of the circuit as a function of time?

An infinitely long wire carrying a current $$I\left( t \right) = {I_0}\cos \left( {\omega t} \right)$$ is placed at a distance a from a square loop of side a as shown in the figure. If the resistance of the loop is R, then the amplitude of the induced current in the loop is

$$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

$$\frac{{{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

$$\frac{{2{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

$$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}$$

A parallel plate capacitor is being discharged. What is the direction of the energy flow in terms of the Poynting vector in the space between the plates?

Along the wire in the positive Z-axis

Radially inward $$\left( { - {\bf{\hat r}}} \right)$$

Radially outward $$\left( {{\bf{\hat r}}} \right)$$

Circumferential $$\left( \phi \right)$$

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

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

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

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

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

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

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

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

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

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

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,

there is no force acting on the dipole

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

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

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

In the circuit shown in the figure, the Thevenin voltage V_Th and Thevenin resistance R_Th as seen by the load resistance R_L (= 1 k$$\Omega $$) are respectively

15 V, 1 k$$\Omega $$

30 V, 4 k$$\Omega $$

20 V, 2 k$$\Omega $$

10 V, 5 k$$\Omega $$

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?

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

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

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

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

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

zero

$$\frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{{m^2}}}{{{d^3}}}$$

$$\frac{{3{\mu _0}}}{{2\pi }} \cdot \frac{{{m^2}}}{{{d^3}}}$$

$$ - \frac{{3{\mu _0}}}{{8\pi }} \cdot \frac{{{m^2}}}{{{d^3}}}$$