Electromagnetism PYQ — Page 59

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement:

Arrange the following electromagnetic radiations per quantum in the order of increasing energy: $A:$ Blue light $B:$ Yellow light $C:$ X-ray $D:$ Radiowave

Three capacitors each of $4 \mu F$ are to be connected in such a way that the effective capacitance is $6 \mu F$. This can be done by connecting them

A series $LR$ circuit is connected to a voltage source with $V(t)={V}_{0}\mathrm{sin}(\omega t)$ . After a very large time, current $I(t)$ behaves as $({t}_{0}\gg \frac{L}{R})$:

A $50 \Omega$ resistance is connected to a battery of $5V$. A galvanometer of resistance $100 \Omega$ is to be used as an ammeter to measure current through the resistance, for this a resistance ${r}_{S}$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is with in $1%$ of the current without the ammeter in the circuit?

A conducting metal circular-wire-loop of radius $r$ is placed perpendicular to a magnetic field which varies with time as $B={B}_{0}{e}^{-\frac{t}{\tau }},$ where ${B}_{0} \mathrm{and} \tau$ are constants at time $t=0$. If the resistance of the loop is $R$, then the heat generated in the loop after a long time $(t\rightarrow \infty )$ is

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4 \mu F$ and $9 \mu F$ capacitors), at a point distant 30 m from it, would equal: 

When $5V$ potential difference is applied across a wire of length $0.1m$, the drift speed of electrons is $2.5\times {10}^{-4} m{s}^{-1}$ . If the electron density in the wire is $8\times {10}^{28} {m}^{-3}$ , the resistivity of the material is close to:

In the given circuits $(a)$ and $(b)$, switches ${\text{S}}_{1}$ and ${\text{S}}_{2}$ are closed at $\text{t}=0$ and kept close for a long time. The variation of currents in the two circuits for $\text{t}\geq 0$ are shown in the options. (Figures are schematic and not drawn to scale.) 

In the electric network shown, when no current flows through the $4 \Omega$ resistor in the arm EB, the potential difference between the points A and D will be: 

In the given circuit, charge ${Q}_{2}$ on the $2\mu F$ capacitor changes as C is varied from $1\mu F$ to $3\mu F$. ${Q}_{2}$ as a function of 'C' is given properly by: (figures are drawn schematically and are not to scale) 

A wire carrying current $I$ is tied between points $P$ and $Q$ and is in the shape of a circular arc of radius $R$ due to a uniform magnetic field $B$ (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle $2{\theta }_{o}$ at the center of the circle (of which it forms an arch) then the tension in the wire is: 

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\vec{{F}_{1}}$ be the magnetic force on the inner solenoid due to the outer one and $\vec{{F}_{2}}$ be the magnetic force on the outer solenoid due to the inner one. Then:

Suppose the drift velocity ${v}_{d}$ in a material varied with the applied electric field E as ${v}_{d }\propto \sqrt{E}$. Then $V-I$ graph for a wire made of such a material is best given by:

The AC voltage across a resistance can be measured using a:

A red $LED$ emits light at $0.1\mathrm{watt}$ uniformly around it. The amplitude of the electric field of the light at a distance of $1m$ from the diode is:

A rectangular loop of sides $10\mathrm{cm}$ and $5\mathrm{cm}$, carrying a current $I$ of $12A$, is placed in different orientations as shown in the figure below. (a)  (b)  (c)  (d)  If there is a uniform magnetic field of $0.3T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(\mathrm{ii})$ unstable equilibrium?

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $–\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to ${Q}_{0}$ and then connected to the L and R as shown below:  If a student plots graphs of the square of maximum charge $({Q}_{Max}^{2})$ on the capacitor with time (t) for two different values ${L}_{1}$ and ${L}_{2}({L}_{1}>{L}_{2})$ of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor ${C}^{'}$ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor ${C}^{'}$ , must have been connected in: 

A uniformly charged solid sphere of radius R has potential ${V}_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3{V}_{0}}{2},\frac{5{V}_{0}}{4},\frac{3{V}_{0}}{4}$ and $\frac{{V}_{0}}{4}$ have radius ${R}_{1}$ , ${R}_{2}, {R}_{3}$ and ${R}_{4}$ respectively. Then Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

Two long straight parallel wires, carrying (adjustable) currents ${I}_{1}$ and ${I}_{2}$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product ${I}_{1}{I}_{2}$ , would be:

In the figure is shown a system of four capacitors connected across a $10V$ battery. The charge that will flow from switch S when it is closed is: 

An electromagnetic wave travelling in the $x-$ direction has frequency of $2\times {10}^{14}Hz$ and electric field amplitude of $27V{m}^{–1}$ oscillates in $Y-$direction. From the options given below, which one describes the magnetic field for this wave?