Q25. Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac { x \sigma } { \epsilon _ { o } }$. The value of $x$ is $\_\_\_\_$ (all quantities are measured in SI units). [Figure]

Q25. A capacitor of $10 \mu \mathrm {~F}$ capacitance whose plates are separated by 10 mm through air and each plate has area $4 \mathrm {~cm} ^ { 2 }$ is now filled equally with two dielectric media of $\mathrm { K } _ { 1 } = 2 , \mathrm {~K} _ { 2 } = 3$ respectively as shown in figure. If new force between the plates is 8 N . The supply voltage is $\_\_\_\_$ $\times 10 ^ { - 4 } \mathrm {~V}$. [Figure] (we modified language of question to make it correct)

Q25. An electric field, $\overrightarrow { \mathrm { E } } = \frac { 2 \hat { i } + 6 \hat { j } + 8 \hat { k } } { \sqrt { 6 } }$ passes through the surface of $4 \mathrm {~m} ^ { 2 }$ area having unit vector $\hat { n } = \left( \frac { 2 \hat { i } + \hat { j } + \hat { k } } { \sqrt { 6 } } \right)$. The electric flux for that surface is $\_\_\_\_$ Vm.

Q25. If the net electric field at point P along Y axis is zero, then the ratio of $\left| \frac { q _ { 2 } } { q _ { 3 } } \right|$ is $\frac { 8 } { 5 \sqrt { x } }$, where $x =$ $\_\_\_\_$ . [Figure]

Q25. At the centre of a half ring of radius $\mathrm { R } = 10 \mathrm {~cm}$ and linear charge density $4 \mathrm { nCm } ^ { - 1 }$, the potential is $x \pi \mathrm {~V}$. The value of $x$ is $\_\_\_\_$

Q25. A particle of mass 0.50 kg executes simple harmonic motion under force $F = - 50 \left( \mathrm { Nm } ^ { - 1 } \right) x$. The time period of oscillation is $\frac { x } { 35 } \mathrm {~s}$. The value of $x$ is $\_\_\_\_$ (Given $\pi = \frac { 22 } { 7 }$ )

Q26. Twelve wires each having resistance $2 \Omega$ are joined to form a cube. A battery of 6 V emf is joined across point [Figure] $a$ and $c$. The voltage difference between $e$ and $f$ is $\_\_\_\_$ V.

Q26. Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of 2.0 mm and wire $B$ has radius of 4.0 mm . The resistance of wire $B$ is $2 \Omega$. The resistance of wire $A$ is $\_\_\_\_$ $\Omega$.

Q26. In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $1 / \theta$ vs the resistance ( $R$ ) of the resistance box is shown in the figure. The figure of merit of the galvanometer is $\_\_\_\_$ [Figure] $\times 10 ^ { - 1 } \mathrm {~A}$ / division. [The source has emf 2V]

Q26. A wire of resistance $20 \Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is $\_\_\_\_$ $\Omega$.

Q26. A wire of resistance $R$ and radius $r$ is stretched till its radius became $r / 2$. If new resistance of the stretched wire is $x R$, then value of $x$ is $\_\_\_\_$

Q26. In the given figure an ammeter A consists of a $240 \Omega$ coil connected in parallel to a $10 \Omega$ shunt. The reading of [Figure] the ammeter is mA

Q26. Resistance of a wire at $0 ^ { \circ } \mathrm { C } , 100 ^ { \circ } \mathrm { C }$ and $t ^ { \circ } \mathrm { C }$ is found to be $10 \Omega , 10.2 \Omega$ and $10.95 \Omega$ respectively. The temperature $t$ in Kelvin scale is $\_\_\_\_$

Q26. A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W , [Figure] the value of $R$ should be $\_\_\_\_$ $\Omega$.

Q26. The current flowing through the $1 \Omega$ resistor is $\frac { n } { 10 } \mathrm {~A}$. The value of $n$ is $\_\_\_\_$ [Figure]

Q26. An electric field $\vec { E } = ( 2 x \hat { i } ) N C ^ { - 1 }$ exists in space. A cube of side 2 m is placed in the space as per figure given [Figure] below. The electric flux through the cube is $\_\_\_\_$ $\mathrm { Nm } ^ { 2 } / \mathrm { C }$.

Q27. The magnetic field existing in a region is given by $\vec { B } = 0.2 ( 1 + 2 x ) \hat { k } \mathrm {~T}$. A square loop of edge 50 cm carrying 0.5 A current is placed in $x - y$ plane with its edges parallel to the $x - y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is $\_\_\_\_$ mN . [Figure]

Q27. Two parallel long current carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac { x } { 7 }$. The value of $x$ is $\_\_\_\_$ [Figure]

Q27. A 2 A current carrying straight metal wire of resistance $1 \Omega$, resistivity $2 \times 10 ^ { - 6 } \Omega \mathrm {~m}$, area of cross-section $10 \mathrm {~mm} ^ { 2 }$ and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field $\vec { B }$. The magnitude of $B$ is $\_\_\_\_$ $\times 10 ^ { - 1 } \mathrm {~T}$ (given, $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ).

Q27. A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' m ' number of turns. It carries a current of 5 A . If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10 ^ { - 3 } \mathrm {~T}$ then the value of $m$ is $\_\_\_\_$ .

Q27. A circular coil having 200 turns, $2.5 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ area and carrying $100 \mu \mathrm {~A}$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $( \vec { M } )$ was directed along $\vec { B }$. Amount of work, required to rotate the coil through $90 ^ { \circ }$ from its initial orientation such that $\vec { M }$ becomes perpendicular to $\vec { B }$, is $\_\_\_\_$ $\mu \mathrm { J }$.

Q27. A coil having 100 turns, area of $5 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 }$, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90 ^ { \circ }$ is $\_\_\_\_$ $\mu \mathrm { J }$.

Q27. An electron with kinetic energy 5 eV enters a region of uniform magnetic field of $3 \mu \mathrm {~T}$ perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of $E$, so that electron moves along the same path, is $\_\_\_\_$ $\mathrm { NC } ^ { - 1 }$. (Given, mass of electron $= 9 \times 10 ^ { - 31 } \mathrm {~kg}$ , electric charge $= 1.6 \times 10 ^ { - 19 } \mathrm { C }$ )

Q27. The coercivity of a magnet is $5 \times 10 ^ { 3 } \mathrm {~A} / \mathrm { m }$. The amount of current required to be passed in a solenoid of length 30 cm and the number of turns 150 , so that the magnet gets demagnetised when inside the solenoid is $\_\_\_\_$ A.

Q27. A square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the $x y$ axis. A magnetic field is passing through the $x - y$ plane and expressed as $\vec { B } = B _ { 0 } ( 1 + 4 x ) \hat { k }$, where $B _ { 0 } = 5 \mathrm {~T}$. The net magnetic force experienced by the loop is $\_\_\_\_$ N.