JEE Magnetic Effects of Current PYQs with Video Solutions PDF

A metal sample carrying a current along X-axis with density $$J_x$$ is subjected to a magnetic field $$B_z$$ (along z-axis). The electric field $$E_y$$ developed along Y-axis is directly proportional to $$J_x$$ as well as $$B_z$$. The constant of proportionality has SI unit.

Choose the correct sketch of the magnetic field lines of a circular current loop shown by the dot and the cross $$\otimes$$.

As shown in the figure, a metallic rod of linear density 0.45 kg m$$^{-1}$$ is lying horizontally on a smooth incline plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 T magnetic field is acting on it in the vertical upward direction, will be (Use $$g = 10$$ m s$$^{-2}$$)

A beam of protons with speed $$4 \times 10^5$$ m s$$^{-1}$$ enters a uniform magnetic field of 0.3 T at an angle of 60$$°$$ to the magnetic field, the pitch of the resulting helical path of protons is close to: (Mass of the proton $$= 1.67 \times 10^{-27}$$ kg, charge of the proton $$= 1.69 \times 10^{-19}$$ C)

An electric current is flowing through a circular coil of radius R. The ratio of the magnetic field at the centre of the coil and that at a distance $$2\sqrt{2}R$$ from the centre of the coil and on its axis is :

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is

A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. lf g is acceleration due to gravity then the acceleration (n) of the charged particle will satisfy :

A charge of $$4.0 \;\mu$$C is moving with a velocity of $$4.0 \times 10^6 \text{ m s}^{-1}$$ along the positive $$y$$-axis under a magnetic field $$B$$ of strength $$\left(2\hat{k}\right)$$ T. The force acting on the charge is $$x\hat{i}$$ N. The value of $$x$$ is ______.

A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is ______ and their speed is ______ in the ratio.

There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is 1:1. The magnetic field at point P is:

The electric current in a circular coil of four turns produces a magnetic induction $$32$$ T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be:

A moving coil galvanometer of resistance $$100\Omega$$ shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is ____ $$\Omega$$

Figure A and B shown two long straight wires of circular cross-section ($$a$$ and $$b$$ with $$a < b$$), carrying current $$I$$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $$B$$ varies with radius $$r$$ and can be represented as:

The current sensitivity of a galvanometer can be increased by:
(A) decreasing the number of turns
(B) increasing the magnetic field
(C) decreasing the area of the coil
(D) decreasing the torsional constant of the spring
Choose the most appropriate answer from the options given below:

The magnetic field at the centre of a current carrying circular loop of radius R is $$16\mu T$$. The magnetic field at a distance $$x = \sqrt{3}R$$ on its axis from the centre is______$$\mu T$$.

A rectangular loop of sides 10 cm and 5 cm, carrying a current $$I$$ of 12 A, is placed in different orientations as shown in the figures below.

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

1 $$\mu$$C charge moving with velocity $$\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$$ m/s in the region of magnetic field $$\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$$ T. The magnitude of force acting on it is $$\sqrt{\alpha} \times 10^{-6}$$ N. The value of $$\alpha$$ is __________.

This question has Statement I and Statement II . Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I : Higher the range, greater is the resistance of ammeter.
Statement - II : To increase the range of ammeter, additional shunt needs to be used across it.

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If $$r_d$$ and $$r_p$$ are the radii of their circular paths respectively, then the ratio $$\frac{r_d}{r_p}$$ will be $$\sqrt{x} : 1$$ where $$x$$ is ______

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $$= 1.6 \times 10^{-19}$$ C)

Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of $$\sigma_0$$. The separation between any two consecutive sheets is $$1 \, \mu$$m. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If $$\sigma_0 = 9 \, \mu$$C/m$$^2$$, then which of the following statements is/are correct:

(Take permittivity of free space $$\epsilon_0 = 9 \times 10^{-12}$$ F/m)

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is released at a distance "a" from the wire with a speed $$\epsilon_{\circ}$$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [$$\mu_{\circ}$$ is vacuum permeability]

A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is $$\vec{B} = (3\hat{i} + 4\hat{k})$$ T. The quantity of flux through the loop ABCDEFA (in Wb) is

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $$\omega$$ with respect to normal axis then magnetic moment of the loop is:

Two long parallel conductors $$S_1$$ and $$S_2$$ are separated by a distance $$10$$ cm and carrying currents of $$4$$ A and $$2$$ A respectively. The conductors are placed along $$x$$-axis in $$X-Y$$ plane. There is a point $$P$$ located between the conductors (as shown in figure).
A charge particle of $$3\pi$$ coulomb is passing through the point $$P$$ with velocity $$\vec{v} = (2\hat{i} + 3\hat{j})$$ m s$$^{-1}$$.
The force acting on the charge particle is $$4\pi \times 10^{-5}(-x\hat{i} + 2\hat{j})$$ N. The value of $$x$$ is

A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic field $$\vec{B}$$ pointing out of the plane of the paper. A clockwise current is set up such that $$i > mg/Ba$$, where a is the width of the loop. Then :

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

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

An electron moves through a uniform magnetic field $$\vec{B} = B_0\hat{i} + 2B_0\hat{j}$$ T. At a particular instant of time, the velocity of electron is $$\vec{u} = 3\hat{i} + 5\hat{j} \text{ m s}^{-1}$$. If the magnetic force acting on electron is $$\vec{F} = 5e\hat{k}$$ N, where $$e$$ is the charge of electron, then the value of $$B_0$$ is ____ T.

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 $$\vec{B} = B_0(1 + 4x)\hat{k}$$, where $$B_0 = 5$$ T. The net magnetic force experienced by the loop is _______ N.