Electromagnetism PYQ — Page 42

A coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at centre, when a current $I$ passes through coil :

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

Figure shows a rod $AB$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge$(-Q)$ is uniformly distributed over rod $\mathrm{AB}$. What is the electric filed $\vec{E}$ at the centre of curvature $O$ ? 

Two small spheres each of mass $10\mathrm{mg}$ are suspended from a point by threads $0.5m$ long. They are equally charged and repel each other to a distance of $0.20m$. The charge on each of the sphere is $\frac{a}{21}\times {10}^{-8}C.$ The value of $a$ will be ___.[Given $g=10m{s}^{-2}$]

An infinite number of point charges, each carrying $1\mu C$ charge, are placed along the y-axis at $y=1m,2m,4m,8m....$ The total force on a $1C$ point charge, placed at the origin, is $x\times {10}^{3}N$. The value of $x$, to the nearest integer, is ___ . [Take $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$]

The electric field intensity is produced by the radiation coming from a $100W$ bulb at a distance of $3m$ is $E$. The electric field intensity produced by the radiation coming from $60W$ at the same distance is $\sqrt{\frac{x}{5}}E$. Where the value of $x=$_________ .

Given below are two statements Statement $I$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere. Statement $\mathrm{II}$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r(<R)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not In the light of the above statements, choose the correct answer from the options given below:

In the given figure switches ${S}_{1}$ and ${S}_{2}$ are in open condition. The resistance across $ab$ when the switches ${S}_{1}$ and ${S}_{2}$ are closed is ________$\Omega .$ 

What equal length of an iron wire and a copper-nickel alloy wire, each of $2\mathrm{mm}$ diameter connected parallel to give an equivalent resistance of $3\Omega$? (Given resistivities of iron and copper-nickel alloy wire are $12\mu \Omega \mathrm{cm}$ and $51\mu \Omega \mathrm{cm}$ respectively)

In an electric circuit, a call of certain emf provides a potential difference of $1.25V$ across a load resistance of $5\Omega .$ However, it provides a potential difference of $1V$ across a load resistance of $2\Omega .$The emf of the cell is given by $\frac{x}{10}V.$ Then the value of $x$ is $.$

In the experiment of Ohm's law, a potential difference of $5.0V$ is applied across the end of a conductor of length $10.0\mathrm{cm}$ and diameter of $5.00\mathrm{mm}.$ The measured current in the conductor is $2.00A.$ The maximum permissible percentage error in the resistivity of the conductor is :-

The energy dissipated by a resistor is $10\mathrm{mJ}$ in $1s$, when an electric current of $2\mathrm{mA}$ flows through it. The resistance is ________$\Omega$. (Round off to the Nearest Integer)

A current of $10A$ exists in a wire of cross-sectional area of $5{\mathrm{mm}}^{2}$ with a drift velocity of $2\times {10}^{-3}{ms}^{-1}.$ The number of free electrons in each cubic meter of the wire is

A current through a wire depends on time as $i={\alpha }_{0}t+\beta {t}^{2}$, where ${\alpha }_{0}=20A{s}^{-1}$ and $\beta =8A{s}^{-2}$. Find the charge crossed through a section of the wire in $15s.$

In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85\times {10}^{-2}A{m}^{-2}$ and moment of inertia $5\times {10}^{-6}\mathrm{kg}{m}^{2}.$ If it performs $10$ complete oscillations in $5$ seconds then the magnitude of the magnetic field is ____$\mathrm{mT}$ [Take ${\pi }^{2}$ as $9.85]$

A plane electromagnetic wave with a frequency of $30\mathrm{MHz}$ travels in free space. At a particular point in space and time, the electric field is $6V{m}^{-1}$. The magnetic field at this point will be $x\times {10}^{-8}T$. The value of $x$ is,

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let ${r}_{d}$ and ${r}_{\alpha }$ be their respective radii of circular path. The value of $\frac{{r}_{d}}{{r}_{\alpha }}$ is equal to:

In the figure given, the electric current flowing through the $5k\Omega$ resistor is $x$ $\mathrm{mA}$.  The value of $x$ to the nearest integer is ________.

A small square loop of side $a$ and one turn is placed inside a larger square loop of side $b$ and one turn $(b\gg a).$ The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side $b,$ then the coefficient of mutual inductance between the two loops is :

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$ components.

A point charge of $+12\mu C$ is at a distance $6\mathrm{cm}$ vertically above the centre of a square of side $12\mathrm{cm}$ as shown in figure. The magnitude of the electric flux through the square will be _______ $\times {10}^{3}N{m}^{2}{C}^{-1}.$ 

In a ferromagnetic material, below the curie temperature, a domain is defined as:

Three capacitors ${C}_{1}=2\mu F,{C}_{2}=6\mu F$ and ${C}_{3}=12\mu F$ are connected as shown in the figure. Find the ratio of the charges on capacitors ${C}_{1},{C}_{2}$ and ${C}_{3}$ respectively. 

A cylindrical wire of radius $0.5\mathrm{mm}$ and conductivity $5\times {10}^{7}S{m}^{-1}$ is subjected to an electric field of $10\mathrm{mV}{m}^{-1}.$ The expected value of current in the wire will be ${x}^{3}\pi \mathrm{mA}.$ The value of $x$ is _________.