Electromagnetism PYQ — Page 6

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$ N/C. The work done in moving the charge is _______ J.

Two resistors of $200 \, \Omega$ and $400 \, \Omega$ are connected in series with a battery of $100$ V. A bulb rated at $200$ V, $100$ W is connected across the $400 \, \Omega$ resistance. The potential drop across the bulb is _______ V.

Two shorts dipoles $(A, B), A$ having charges $\pm 2 \mu \mathrm{C}$ and length 1 cm and $B$ having charges $\pm 4 \mu \mathrm{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the centres of both dipoles is $\_\_\_\_$ N/C. 

A meter bridge with two resistances $R_{1}$ and $R_{2}$ as shown in figure was balanced (null point) at 40 cm from the point $P$. The null point changed to 50 cm from the point $P$, when $16 \Omega$ resistance is connected in parallel to $R_{2}$. The values of resistances $R_{1}$ and $R_{2}$ are $\_\_\_\_$. 

The electric potential as a function of $x, y$ is given by $V = 5(x^2 - y^2)$ V. The electric field at a point $(2, 3)$ m is __________ V/m.

Under steady state condition the potential difference across the capacitor in the circuit is _______ V. 

A small cube of side $1$ mm is placed at the centre of a circular loop of radius $10$ cm carrying a current of $2$ A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is _______. ($\mu_o = 4\pi \times 10^{-7}$ Tm/A, $\pi = 3.14$)

Two charges $7 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$ are placed at $(-9,0,0) \mathrm{cm}$ and $(9,0,0) \mathrm{cm}$ respectively in an external field $E=\frac{\mathrm{A}}{r^{2}} \hat{r}$, where $A=9 \times 10^{5} \mathrm{~N} / \mathrm{C}. \mathrm{m}^{2}$. Considering the potential at infinity is 0, the electrostatic energy of the configuration is $\_\_\_\_$ J.

Two resistors $2 \Omega$ and $3 \Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire $X Y$. When an unknown resistor is connected in parallel with $3 \Omega$ resistor, the null point is shifted by 22.5 cm toward $Y$. The resistance of unknown resistor is $\_\_\_\_$ $\Omega$. 

Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential $(V)$ and the electric field $(\vec{E})$ at the center $O$ of the pentagon due to these five positive charges are: 

A long straight wire carries a current of 10 A. The magnetic field at a distance of 0.1 m from the wire is:

Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ($k_{1}$ and $k_{2}$) in the following fashion. Which of the following is true? $\left(k_{1}>k_{2}\right)$ 

A conducting circular loop of area $1.0 \mathrm{~m}^{2}$ is placed perpendicular to a magnetic field which varies as $B=\sin (100 t)$ Tesla. If the resistance of the loop is $100 \Omega$, then the average thermal energy dissipated in the loop in one period is $\_\_\_\_$ J.

$1\,\mu$C charge moving with velocity $\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$ m/s in the region of magnetic field $\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{-6}$ N. The value of $\alpha$ is _______.

The stored charge in the capacitor in steady state of the following circuit is ________ $\mu$C. 

A displacement current of $4.0$ A can be set up in the space between two parallel plates of $6$ $\mu$F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^6$ V/s. The value of $\alpha$ is __________.

$X P Q Y$ is a vertical smooth long loop having a total resistance $R$ where $P X$ is parallel to $Q Y$ and separation between them is $l$. A constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. A rod $C D$ of length $L(L>l)$ and mass $m$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}.(\mathrm{g}=$ acceleration due to gravity) 

A thin half ring of radius $35$ cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100$ V/m, then the value of $Q$ is _______ nC. ($\epsilon_o = 8.85 \times 10^{-12}$ C$^2$/Nm$^2$ and $\pi = 3.14$)

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances $\left(R_{1}=R_{2}=R_{3}=R_{4}\right)$. When $R_{3}$ resistance is heated to some temperature, its resistance value has gone up by $10 \%$. The potential difference $\left(V_{a}-V_{b}\right)$ (after $R_{3}$ is heated) is $\_\_\_\_$ V. 

An inductor of inductance $10$ mH having resistance of $100\,\Omega$ is connected to battery of E.M.F. $1.0$ V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is $2$ mA and $4$ mA is _______. 

A moving coil of galvanometer when shunted with $2\,\Omega$ resistance gives a full scale deflection for a current of $500$ mA. When a resistance of $470\,\Omega$ is connected in series it gives a full scale deflection for $10$ V potential applied on it. The value of resistance of galvanometer coil is __________ $\Omega$.

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $10 \pi \mathrm{rad} \mathrm{s}^{-1}$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? $(\pi=3.14)$

A particle of charge $q$, mass $m$ and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius( r). Which of the following curves represents the variation of $r$ with $E$ ?