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Match List I with List II.

Choose the correct answer from the options given below:

With the help potentiometer, we can determine the value of emf of given cell. The sensitivity of the potentiometer is:
(A) Directly proportional to the length of the potentiometer wire.
(B) Directly proportional to the potential gradient of the wire.
(C) Inversely proportional to the potential gradient of the wire.
(D) Inversely proportional to the length of the potentiometer wire.
Choose the correct option for the above statements

A charge particle of \( 2\mu \text{C} \) accelerated by a potential difference of \( 100 \, \text{V} \) enters a region of uniform magnetic field of magnitude \( 4 \, \text{mT} \) at right angle to the direction of field. The charge particle completes semicircle of radius \( 3 \, \text{cm} \) inside magnetic field. The mass of the charge particle is \( \_\_\_\_\_ \times 10^{-18} \) \( \text{kg} \).

The free space inside a current carrying toroid is filled with a material of susceptibility \( 2 \times 10^{-2} \). The percentage increase in the value of magnetic field inside the toroid will be:

A single turn current loop in the shape of a right angle triangle with sides \( 5 \, \text{cm} \), \( 12 \, \text{cm} \), \( 13 \, \text{cm} \) is carrying a current of \( 2 \, \text{A} \). The loop is in a uniform magnetic field of magnitude \( 0.75 \, \text{T} \) whose direction is parallel to the current in the \( 13 \, \text{cm} \) side of the loop. The magnitude of the magnetic force of the \( 5 \, \text{cm} \) side will be \( \frac{x}{130} \, \text{N} \). The value of \( x \) is ________.

A circular loop of radius \( r \) is carrying current \( 1 \, \text{A} \). The ratio of magnetic field at the centre of circular loop and at a distance \( r \) from the center of the loop on its axis is:

A single current carrying loop of wire carrying current \( I \) flowing in anticlockwise direction seen from \( +ve \) \( z \) direction and lying in \( xy \) plane is shown in figure. The plot of \( \, \hat{\jmath} \, \) component of magnetic field \( (B_y) \) at a distance \( a\) (less than radius of the coil) and on \( yz \) plane vs \( z \) coordinate looks like:

The elastic potential energy stored in a steel wire of length \( 20 \, \text{m} \) stretched through \( 2 \, \text{cm} \) is \( 80 \, \text{J} \). The cross sectional area of the wire is ________ \( \text{mm}^2 \). (given \( y = 2.0 \times 10^{11} \, \text{Nm}^{-2} \))

Two long straight wires \( P \) and \( Q \) carrying equal current \( 10 \, \text{A} \) each were kept parallel to each other at \( 5 \, \text{cm} \) distance. Magnitude of magnetic force experienced by \( 10 \, \text{cm} \) length of wire \( P \) is \( F_1 \). If distance between wires is halved and currents on them are doubled, force \( F_2 \) on \( 10 \, \text{cm} \) length of wire \( P \) will be:

A proton with a kinetic energy of \( 2.0 \, \text{eV} \) moves into a region of uniform magnetic field of magnitude \( \dfrac{\pi}{2} \times 10^{-3} \, \text{T} \). The angle between the direction of magnetic field and velocity of proton is \( 60^\circ \). The pitch of the helical path taken by the proton is ________ \( \text{cm} \). (Take, mass of proton \( = 1.6 \times 10^{-27} \, \text{kg} \) and Charge on proton \( = 1.6 \times 10^{-19} \, \text{C} \).)

An aluminium rod with Young’s modulus \( Y = 7.0 \times 10^{10} \, \text{N}/\text{m}^{2} \) undergoes elastic strain of \( 0.04\% \). The energy per unit volume stored in the rod in SI unit is:

The length of a metallic wire is increased by \( 20\% \) and its area of cross section is reduced by \( 4\% \). The percentage change in resistance of the metallic wire is ______________.

The magnitude of magnetic induction at mid point \( O \) due to current arrangement as shown in figure will be:

A null point is found at \( 200 \, \text{cm} \) is potentiometer when cell in secondary circuit is shunted by \( 5\,\Omega \). When a resistance of \( 15\,\Omega \) is used for shunting, null point moves to \( 300 \, \text{cm} \). The internal resistance of the cell is __________ \( \Omega \).

A straight wire carrying a current of \( 14 \, \text{A} \) is bent into a semicircular arc of radius \( 2.2 \, \text{cm} \) as shown in the figure. The magnetic field produced by the current at the centre \( (O) \) of the arc, is ______ \( \times 10^{-4} \, \text{T} \).

As shown in the figure, a long straight conductor with semicircular arc of radius \( \frac{\pi}{10} \, \text{m} \) is carrying current \( I = 3 \, \text{A} \). The magnitude of the magnetic field, at the centre O of the arc is:
(The permeability of the vacuum \( = 4\pi \times 10^{-7} \, \text{N A}^{-2} \).)

A charge particle moving in magnetic field \( B \), has the components of velocity along \( B \) as well as perpendicular to \( B \). The path of the charge particle will be:

Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

The magnetic moments associated with two closely wound circular coils \( A \) and \( B \) of radius \( r_{A} = 10 \, \text{cm} \) and \( r_{B} = 20 \, \text{cm} \) respectively are equal if: (Where \( N_{A}, I_{A} \) and \( N_{B}, I_{B} \) are number of turn and current of \( A \) and \( B \) respectively)

A long solenoid is formed by winding \( 70 \) turns \( \text{cm}^{-1} \). If \( 2.0 \, \text{A} \) current flows, then the magnetic field produced inside the solenoid is __________ \( (\mu = 4\pi \times 10^{-7} \, \text{TmA}^{-1}) \)

Two long parallel wires carrying currents \( 8 \, \text{A} \) and \( 15 \, \text{A} \) in opposite directions are placed at a distance of \( 7 \, \text{cm} \) from each other. A point \( P \) is at equidistant from both the wires such that the lines joining the point \( P \) to the wires are perpendicular to each other. The magnitude of magnetic field at \( P \) is _____ \( \times 10^{-6} \, \text{T} \). \( \left( \text{Given} : \sqrt{2} = 1.4 \right) \).

A compass needle oscillates \( 20 \) times per minute at a place where the dip is \( 30^{\circ} \) and \( 30 \) times per minute where the dip is \( 60^{\circ} \). The ratio of total magnetic field due to the earth at two places respectively is \( \dfrac{4}{\sqrt{x}} \). The value of \( x \) is:

The magnetic intensity at the centre of a long current carrying solenoid is found to be \( 1.6 \times 10^3 \, \text{A m}^{-1} \). If the number of turns is \( 8 \) per cm, then the current flowing through the solenoid is ________ \( \text{A} \).

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JEE Main 2023 8th April Morning Shift

An aluminium rod with Young’s modulus \( Y = 7.0 \times 10^{10} \, \text{N}/\text{m}^{2} \) undergoes elastic strain of \( 0.04\% \). The energy per unit volume stored in the rod in SI unit is: