Electromagnetism PYQ — Page 52

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure: 

A power transmission line feeds input power at $2300 V$ to a step down transformer with its primary windings having $4000$ turns. The output power is delivered at $230 V$ by the transformer. If the current in the primary of the transformer is $5A$ and its efficiency is $90%$, the output current would be:

A conducting circular loop made of a thin wire has area $3.5\times {10}^{-2} {m}^{2}$ and resistance $10 \Omega$ It is placed perpendicular to a time-dependent magnetic field $B(t)=(0.4T)\mathrm{sin}⁡(50\pi t)$ The field is uniform in space. Then the net charge flowing through the loop during $t=0 s$ and $t=10 \mathrm{ms}$ is close to

A square loop is carrying a steady current $I$ and the magnitude of its magnetic dipole moment is $m$ . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side $1 m$ which is carrying a current of $10 A$ is: [Take ${\mu }_{0}=4\pi \times {10}^{-7} N {A}^{-2}$ ]

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10 A.$ The magnetic field at point $O$ will be close to: 

In the given circuit the cells have zero internal resistance. The currents (in amperes) passing through resistance ${R}_{1}$ and ${R}_{2}$ respectively, are: 

There is a uniform spherically symmetric surface charge density at a distance ${R}_{0}$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $V(R(t))$ of the distribution as a function of its instantaneous radius $R(t)$ is:

A uniform metallic wire has a resistance of $18\Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is:

A magnet of total magnetic moment ${10}^{-2}\hat{i} A{m}^{2}$ is placed in a time varying magnetic field, $B\hat{i}(\mathrm{cos}\omega t)$ where $B=1$ Tesla and $\omega =0.125 \mathrm{rad}{s}^{-1}$. The work done for reversing the direction of the magnetic moment at $t=1$ second, is:

Two very long, straight, and insulated wires are kept at ${90}^{o}$ angle from each other in $xy-plane$ as shown in figure.  These wires carry currents of equal magnitude $I$ , whose direction are shown in the figure. The net magnetic field at point $P$ will be:

A plane electromagnetic wave of frequency $50 MHz$ travels in free space along the positive $x$ - direction. At a particular point in space and time, $\vec{E}=6.3 \hat{j} V/m,$ The corresponding magnetic field $\vec{B,}$ at that point will be:

If the magnetic field of a plane electromagnetic wave is given by (The speed of light $=3\times {10}^{8} m/s$) $B=100\times {10}^{-6}\mathrm{sin}⁡[2\pi \times 2\times {10}^{15}(t-\frac{x}{c})]$ then the maximum electric field associated with it is:

Two wires $A$ & $B$ are carrying currents ${I}_{1}$ and ${I}_{2}$ as shown in the figure. The separation between them is $d$ . A third wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from $A$ such that the net force acting on it is zero. The possible values of $x$ are: 

A thin ring of $10 cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi rad{s}^{-1}$ about its axis, perpendicular to its plane. Is the magnetic field its centre is $3.8\times {10}^{-9}T$ , then the charge carried by the ring is close to $({\mu }_{0}=4\pi \times {10}^{-7}N/{A}^{2}).$

An insulating thin rod of length $l$ has a linear charge density $\rho (x)={\rho }_{0}\frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x=0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second, then the time averaged magnetic moment of the rod is:

A moving coil galvanometer allows a full scale current of ${10}^{-4} A$ . A series resistance of $2 \times {10}^{4} \Omega$ is required to convert the galvanometer into a voltmeter of range $0-5 V$ . Therefore, the value of shunt resistance required to convert the above galvanometer into an ammeter of range $0-10 mA$ is:

A Point dipole $\vec{p}=-{p}_{0}\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y-axis$ at a distance $d$ are, respectively: (Taken $V=0$ at infinity)

A uniformly charged ring of radius $3a$ and total charge $q$ is placed in $x‐y$ plane centred at origin. A point charge $q$ is moving towards the ring along the $z-$ axis and has speed $v$ at $z=4a$ . The minimum value of $v$ such that it crosses the origin is:

Four point charges $-q, +q, +q$ and $-q$ are placed on y-axis at $y=-2d, y=-d,$ and $y=+2d,$ respectively. The magnitude of the electric field $E$ at a point on the x-axis at $x=D,$ with $D\gg d,$ will behave as:

A charge $Q$ is distributed over three concentric spherical shells of radii $a, b, c (a<b<c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre, where $r<a,$ would be:

In a Wheatstone bridge (see fig.), Resistances $P$ and $Q$ are approximatelyequal. When $R=400 \Omega$, the bridge is balanced. On interchanging $\mathrm{P}$ and $\mathrm{Q}$, the value of $\mathrm{R},$ for balance, is $405 \Omega$. The value of $Y$ is close to 

Seven capacitors, each of capacitance $2 \mu \mathrm{F},$ are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right) \mu \mathrm{F} .$ Which of the combinations, shown in figures below, will achieve the desired value?

A cell of internal resistance $r$ drives current through an external resistance $R.$ The power delivered by the cell to the external resistance will be maximum when: