Electromagnetism PYQ — Page 47

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4\mathrm{mm}$ and a total length of $30\mathrm{cm}.$ The magnetic field changes with time at a steady rate $\mathrm{dB}/\mathrm{dt}=0.032{\mathrm{Ts}}^{-1}.$ The induced current in the $loop$is close to (Resistivity of the metal wire is $1.23\times {10}^{-8}\Omega m$ )

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by$\hat{k}$ and $2\hat{i}-2\hat{j}$, respectively. What is the unit vector along direction of propagation of the wave.

Consider a circular coil of wire carrying constant current $I,$ forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${\phi }_{i}$ The magnetic flux through the area of the circular coil area is given by ${\phi }_{0}$ . Which of the following option is correct?

In the given circuit diagram, a wire is joining points B and D. The current in this wire is: 

A galvanometer coil has 500 turns and each turn has an average area of $3\times {10}^{-4}{m}^{2}$. If a torque of $1.5\mathrm{Nm}$ is required to keep this coil parallel to a magnetic field when a current of $0.5A$ is flowing through it, the strength of the field (in $T$) is _________ .

A series $L-R$ circuit is connected to a battery of emf $V$. If the circuit is switched on at $t=0$, then the time at which the energy stored in the inductor reaches $(\frac{1}{n})$ times of its maximum value, is :

A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v}={v}_{0}\hat{j}$ . If an electric field $\vec{E}={E}_{0}\hat{i}$ and magnetic field $\vec{B}={B}_{0}\hat{i}$ act on the particle, its speed will double after a time

In finding the electric field using Gauss law the formula $|\vec{E}|=\frac{{q}_{enc}}{{\epsilon }_{0}|A|}$ is applicable. In the formula ${\epsilon }_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and ${q}_{enc}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

Suppose that intensity of a laser is $(\frac{315}{\pi })W{m}^{-2}.$ The rms electric field, in units of $V{m}^{-1}$ associated with this source is close to the nearest integer is $-({\epsilon }_{0}=8.86\times {10}^{-12}{C}^{2}N{m}^{-2};c=3\times {10}^{8}m{s}^{-1})$

A $5\mu F$ capacitor is charged fully by a $220V$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5\mu F$ capacitor. If the energy change during the charge redistribution is $\frac{X}{100}J$ then value of $X$ to the nearest integer is :

A $60pF$ capacitor is fully charged by a $20V$ supply. It is then disconnected from the supply and is connected to another uncharged $60pF$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $nJ$ ) ________

An ideal cell of emf $10V$ is connected in circuit shown in figure. Each resistance is $2\Omega$. The potential difference (in $V$) across the capacitor when it is fully charged is _____________ 

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of $6mA$ it produces a deflection of $2^{\circ}$, its figure of merit is close to :

In the figure shown, the current in the $10V$ battery is close to : 

In a meter bridge experiment $S$ is a standard resistance. $R$ is a resistance wire. It is found that balancing length is $l=25cm.$ If $R$ is replaced by a wire of hall length and half diameter that of $R$ of same material, then the balancing distance $l'$ (in $cm$ ) will now be ______________. 

A galvanometer having a coil resistance $100 \Omega$ gives a full scale deflection when a current of $1mA$ is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter given full scale deflection for a potential difference of $10V?$

A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $\vec{B}$. Then the field inside the paramagnetic substance is: 

Two resistors $400\Omega$ and $800\Omega$ are connected in series across a $6\vee$ battery. The potential difference measured by a voltmeter of $10k\Omega$ across $400\Omega$ resistor is close to:

Two isolated conducting spheres ${S}_{1}$ and ${S}_{2}$ of radius $\frac{2}{3}R$ and $\frac{1}{3}R$ have $12\mu C$ and $-3\mu C$ charges, respectively, and are at a large distance from each other, They are now connected by a conducting wire. A long time after this is done the charges on ${S}_{1}$ and ${S}_{2}$ are respectively:

An elliptical loop having resistance $R$, of semi major axis $a$ , and semi minor axis $b$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$, the average power loss in the loop due to Joule heating is : 

A charged particle carrying charge $1\mu C$ is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k})m{s}^{-1}$. If an external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times {10}^{-3}T$ exists in the region where the particle is moving then the force on the particle is $\vec{F}\times {10}^{-9}N$ . the vector $\vec{F}$ is :

Two charged thin infinite plane sheets of uniform charge density ${\sigma }_{+}$ and ${\sigma }_{-}$, where $|{\sigma }_{+}|>|{\sigma }_{-}|$, intersect at the right angle. Which of the following best represents the electric field lines for the system:

A galvanometer of resistance $G$ is converted into a voltameter of range $0-1V$ by connecting a resistance $R$ in series with it. The additional resistance that should be connected in series with ${R}_{1}$ to increase the range of the voltmeter to $0-2V$ will be :

 The figure gives experimentally measured $B$ vs. $H$ variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are: