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In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

A current of \(200\,\mu\) \(\text{A}\) deflects the coil of a moving coil galvanometer through \(60^{\circ}\). The current to cause deflection through \(\displaystyle\frac{\pi}{10}\) radian is:

Water boils in an electric kettle in \( 20 \) minutes after being switched on. Using the same main supply, the length of the heating element should be __________ to __________ times of its initial length if the water is to be boiled in \( 15 \) minutes.

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

A heater is designed to operate with a power of \( 1000 \,\text{W} \) in a \( 100 \,\text{V} \) line. It is connected in combination with a resistance of \( 10\,\Omega \) and a resistance \( R \), to \( 100 \,\text{V} \) mains as shown in figure. For the heater to operate at \( 62.5 \,\text{W} \), the value of \( R \) should be ______ \( \Omega \).

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \( R_1 = 2\pi \, \text{m} \) and \( R_2 = 4\pi \, \text{m} \), carrying current \( I = 4 \, \text{A} \) as per figure given below is \( \alpha \times 10^{-7} \, \text{T} \). The value of \( \alpha \) is __________ . (Centre O is common for all segments).

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0\text{ cm}$. The magnitude of the magnetic field at a point P midway between the wires is $\underline{\quad}\ \mu\text{T}$ . (Given : $\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$)

A rigid wire consists of a semicircular position of radius \( R \) and two straight sections. The wire is partially immerged in a perpendicular magnetic field \( B = B_0 \hat{k} \) as shown in figure. The magnetic force on the wire if it has current \( i \) is:

An electron moves through a uniform magnetic field $\vec{B} = B_0\hat{i} + 2B_0\hat{j}\text{ T}$. At a particular instant of time, the velocity of electron is $\vec{u} = 3\hat{i} + 5\hat{j}\text{ m/s}$. If the magnetic force acting on electron is $\vec{F} = 5e\hat{k}\text{ N}$, where $e$ is the charge of electron, then the value of $B_0$ is ________ $\text{T}$.

Two circular coils P and Q of \( 100 \) turns each have same radius of \( \pi \, \text{cm} \). The currents in P and R and \( 1 \, \text{A} \) and \( 2 \, \text{A} \) respectively. P and Q are placed with their planes mutually perpendicular with their centres coincide. The resultant magnetic field induction at the centre of the coils is \( \sqrt{x} \, \text{mT} \), where \( x \) _______.
[Use \( \mu_{0} = 4 \pi \times 10^{-7} \, \text{T m A}^{-1} \)]

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

A moving coil galvanometer has \( 100 \) turns and each has an area of \( 2.0 \, \text{cm}^2 \). The magnetic field produced by the magnet is \( 0.01 \, \text{T} \) and the deflection in the coil is \( 0.05 \) radian when a current of \( 10 \, \text{mA} \) is passed through it. The torsional constant of the suspension wire is \( x \times 10^{-5} \, \text{N·m/rad} \). The value of \( x \) is __________.

A regular polygon of \( 6 \) sides is formed by bending a wire of length \( 4\pi \) meter. If an electric current of \( 4\pi \sqrt{3} \, \text{A} \) is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be \( x \times 10^{-7} \, \text{T} \). The value of \( x \) is ______.

A uniform magnetic field of \( 2 \times 10^{-3} \, \text{T} \) acts along positive \( Y \)-direction. A rectangular loop of sides \( 20 \, \text{cm} \) and \( 10 \, \text{cm} \) with current of \( 5 \, \text{A} \) is in \( Y - z \) plane. The current is in anticlockwise sense with reference to negative \( X \) axis. Magnitude and direction of the torque is:

The horizontal component of earth's magnetic field at a place is \( 3.5 \times 10^{-5} \, \text{T} \). A very long straight conductor carrying current of \( \sqrt{2} \, \text{A} \) in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is ______ \( \times 10^{-6} \, \text{N} / \text{m} \).

A galvanometer has a coil of resistance \( 200 \, \Omega \) with a full scale deflection at \( 20 \, \mu \text{A} \). The value of resistance to be added to use it as an ammeter of range \( (0 - 20) \, \text{mA} \) is:

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have :
(A) $\quad E = 0, B = 0$
(B) $\quad E = 0, B \neq 0$
(C) $\quad E \neq 0, B = 0$
(D) $\quad E \neq 0, B \neq 0$

Choose the most appropriate answer from the options given below :

The current of \( 5\,\text{A} \) flows in a square loop of side \( 1\,\text{m} \) is placed in air. The magnetic field at the centre of the loop is \( X\sqrt{2} \times 10^{-7}\ \text{T} \). The value of \( X \) is ______.

Two insulated circular loop A and B of radius \(' a' \) carrying a current of \( 'I' \) in the anti clockwise direction as shown in the fig. The magnitude of the magnetic induction at the centre will be:

A rectangular loop of sides \( 12 \, \text{cm} \) and \( 5 \, \text{cm} \), with its sides parallel to the \( x \)-axis and \( y \)-axis respectively, moves with a velocity of \( 5 \, \text{cm/s} \) in the positive \( x \) axis direction, in a space containing a variable magnetic field in the positive \( z \) direction. The field has a gradient of \( 10^{-3} \, \text{T} / \text{cm} \) along the negative \( x \) direction and it is decreasing with time at the rate of \( 10^{-3} \, \text{T} / \text{s} \). If the resistance of the loop is \( 6 \, \text{m}\Omega \), the power dissipated by the loop as heat is ______ \( \times 10^{-9} \, \text{W} \).

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JEE Main 2024 30th Jan Morning Shift

Two insulated circular loop A and B of radius \(' a' \) carrying a current of \( 'I' \) in the anti clockwise direction as shown in the fig. The magnitude of the magnetic induction at the centre will be: