Core Syllabus Module

Magnetic Effects of Current

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JEE Advanced 2014

LEVELJEE Advanced

Comprehension Passage

The figure shows a circular loop of radius

a

with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is

d

. The loop and the wires are carrying the same current

I

. The current in the loop is in the counter-clockwise direction if seen from above.

Question 1:

When $d \approx a$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case

(A)

currents in wire 1 and wire 2 are in the directions

P Q

and

R S

, respectively and

h \approx a

(B)

currents in wire 1 and wire 2 are in the directions

P Q

and

S R

, respectively and

h \approx a

(C)

currents in wire 1 and wire 2 are in the directions

P Q

and

S R

, respectively and

h \approx 1.2 a

(D)

currents in wire 1 and wire 2 are in the directions

P Q

and

R S

, respectively and

h \approx 1.2 a

Question 2:

Consider $d >> a$ , and the loop is rotated about its diameter parallel to the wires by $3 0^{\circ}$ from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

(A)

\frac{μ _{0} I ^{2} a ^{2}}{d}

(B)

\frac{μ _{0} I ^{2} a ^{2}}{2 d}

(C)

\frac{3 μ _{0} I ^{2} a ^{2}}{d}

(D)

\frac{3 μ _{0} I ^{2} a ^{2}}{2 d}

JEE Advanced 1993

LEVELJEE Advanced

An electron gun $G$ emits electrons of energy $2 keV$ travelling in the positive $x$ -direction. The electrons are required to hit the spot $S$ where $GS = 0.1 m$ , and the line $GS$ makes an angle of $6 0^{\circ}$ with the $x$ -axis as shown in figure. A uniform magnetic field $B$ parallel to $GS$ exists in the region outside the electron gun. Find the minimum value of $B$ needed to make the electrons hit $S$ .

JEE Advanced 2015

LEVELJEE Advanced

Comprehension Passage

In a thin rectangular metallic strip a constant current

I

flows along the positive

x

-direction, as shown in the figure. The length, width and thickness of the strip are

l

w

and

d

, respectively. A uniform magnetic field

B

is applied on the strip along the positive

y

-direction. Due to this, the charge carriers experience a net deflection along the

z

-direction. This results in accumulation of charge carriers on the surface

P QR S

and appearance of equal and opposite charges on the face opposite to

P QR S

. A potential difference along the

z

-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Question 1:

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are $w_{1}$ and $w_{2}$ and thicknesses are $d_{1}$ and $d_{2}$ , respectively. Two points $K$ and $M$ are symmetrically located on the opposite faces parallel to the $x$ - $y$ plane (see figure). $V_{1}$ and $V_{2}$ are the potential differences between $K$ and $M$ in strips 1 and 2, respectively. Then, for a given current $I$ flowing through them in a given magnetic field strength $B$ , the correct statements is/are

* Multiple Correct Options

(A)

w_{1} = w_{2}

and

d_{1} = 2 d_{2}

, then

V_{2} = 2 V_{1}

(B)

w_{1} = w_{2}

and

d_{1} = 2 d_{2}

, then

V_{2} = V_{1}

(C)

w_{1} = 2 w_{2}

and

d_{1} = d_{2}

, then

V_{2} = 2 V_{1}

(D)

w_{1} = 2 w_{2}

and

d_{1} = d_{2}

, then

V_{2} = V_{1}

Question 2:

Consider two different metallic strips (1 and 2) of same dimensions (length $l$ , width $w$ and thickness $d$ ) with carrier densities $n_{1}$ and $n_{2}$ , respectively. Strip 1 is placed in magnetic field $B_{1}$ and strip 2 is placed in magnetic field $B_{2}$ , both along positive $y$ -directions. Then $V_{1}$ and $V_{2}$ are the potential differences developed between $K$ and $M$ in strips 1 and 2, respectively. Assuming that the current $I$ is the same for both the strips, the correct options is/are

* Multiple Correct Options

(A)

B_{1} = B_{2}

and

n_{1} = 2 n_{2}

, then

V_{2} = 2 V_{1}

(B)

B_{1} = B_{2}

and

n_{1} = 2 n_{2}

, then

V_{2} = V_{1}

(C)

B_{1} = 2 B_{2}

and

n_{1} = n_{2}

, then

V_{2} = 0.5 V_{1}

(D)

B_{1} = 2 B_{2}

and

n_{1} = n_{2}

, then

V_{2} = V_{1}

JEE Advanced 2000

LEVELJEE Advanced

A circular loop of radius $R$ is bent along a diameter and given a shape as shown in figure. One of the semicircles ( $K N M$ ) lies in the $x$ - $z$ plane and the other one ( $K L M$ ) in the $y$ - $z$ plane with their centres at origin. Current $I$ is flowing through each of the semicircles as shown in figure. (a) A particle of charge $q$ is released at the origin with a velocity $v = - v_{0} \hat{i}$ . Find the instantaneous force $F$ on the particle. Assume that space is gravity free. (b) If an external uniform magnetic field $B_{0} \hat{j}$ is applied determine the force $F_{1}$ and $F_{2}$ on the semicircles $K L M$ and $K N M$ due to the field and the net force $F$ on the loop.

JEE Advanced 2009

LEVELJEE Advanced

Six point charges, each of the same magnitude $q$ , are arranged in different manners as shown in Column II. In each case, a point $M$ and a line $P Q$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $P Q$ . Let $B$ be the magnetic field at $M$ and $μ$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

List-I

(P)

E = 0

(Q)

V \neq = 0

(R)

B = 0

(S)

μ \neq = 0

List-II

(1)

Charges are at the corners of a regular hexagon.

M

is at the centre of the hexagon.

P Q

is perpendicular to the plane of the hexagon.

(2)

Charges are on a line perpendicular to

P Q

at equal intervals.

M

is the mid-point between the two innermost charges.

(3)

Charges are placed on two coplanar insulating rings at equal intervals.

M

is the common centre of the rings.

P Q

is perpendicular to the plane of the rings.

(4)

Charges are placed at the corners of a rectangle of sides

a

and

2 a

and at the mid points of the longer sides.

M

is at the centre of the rectangle.

P Q

is parallel to the longer sides.

(5)

Charges are placed on two coplanar, identical insulating rings at equal intervals.

M

is the mid points between the centres of the rings.

P Q

is perpendicular to the line joining the centres and coplanar to the rings.

JEE Advanced 1997

LEVELJEE Advanced

Three infinitely long thin wires, each carrying current $i$ in the same direction, are in the $x$ - $y$ plane of a gravity free space. The central wire is along the $y$ -axis while the other two are along $x = \pm d$ . (a) Find the locus of the points for which the magnetic field $B$ is zero. (b) If the central wire is displaced along the $z$ -direction by a small amount and released, show that it will execute simple harmonic motion. If the linear density of the wires is $λ$ , find the frequency of oscillation.

JEE Advanced 1991

LEVELJEE Advanced

A wire loop carrying a current $I$ is placed in the $x$ - $y$ plane as shown in figure. (a) If a particle with charge $+ Q$ and mass $m$ is placed at the centre $P$ and given a velocity $v$ along $N P$ (see figure), find its instantaneous acceleration. (b) If an external uniform magnetic induction field $B = B \hat{i}$ is applied, find the force and the torque acting on the loop due to this field.

JEE Advanced 2025

LEVELJEE Advanced

A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$ . The sphere is rotating about an axis passing through its center with a uniform angular speed $ω$ . The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as $α \frac{Q}{2 M}$ . The value of $α$ is _______.

JEE Main 2019

LEVELJEE Advanced

An electron moving along the X-axis with an initial energy of $100 eV$ , enters a region of magnetic field $B = (1.5 \times 1 0^{- 3} T) \hat{k}$ at $S$ (see figure). The field extends between $x = 0$ and $x = 2 cm$ . The electron is detected at the point $Q$ on a screen placed $8 cm$ away from the point $S$ . The distance $d$ between $P$ and $Q$ (on the screen) is (Take, electron's charge $= 1.6 \times 1 0^{- 19} C$ , mass of electron $= 9.1 \times 1 0^{- 31} kg$ )

In the $x y$ -plane, the region $y > 0$ has a uniform magnetic field $B_{1} \hat{k}$ and the region $y < 0$ has another uniform magnetic field $B_{2} \hat{k}$ . A positively charged particle is projected from the origin along the positive $Y$ -axis with speed $v_{0} = π ms^{- 1}$ at $t = 0$ , as shown in figure. Neglect gravity in this problem. Let $t = T$ be the time when the particle crosses the $X$ -axis from below for the first time. If $B_{2} = 4 B_{1}$ , the average speed of the particle, in $ms^{- 1}$ , along the $X$ -axis in the time interval $T$ is ......... .

JEE Advanced 2017

LEVELJEE Advanced

Comprehension Passage

A charged particle (electron or proton) is introduced at the origin (

x = 0, y = 0, z = 0

) with a given initial velocity

v

. A uniform electric field

E

and a uniform magnetic field

B

exist everywhere. The velocity

v

, electric field

E

and magnetic field

B

are given in columns 1, 2 and 3, respectively. The quantities

E_{0}, B_{0}

are positive in magnitude. $\begin{array}{lll} \hline \text{Column 1} & \text{Column 2} & \text{Column 3} \\ \hline \text{(I) Electron with } \mathbf{v} = 2\frac{E_0}{B_0}\hat{x} & \text{(i) } \mathbf{E} = E_0\hat{z} & \text{(P) } \mathbf{B} = -B_0\hat{x} \\ \text{(II) Electron with } \mathbf{v} = \frac{E_0}{B_0}\hat{y} & \text{(ii) } \mathbf{E} = -E_0\hat{y} & \text{(Q) } \mathbf{B} = B_0\hat{x} \\ \text{(III) Proton with } \mathbf{v} = 0 & \text{(iii) } \mathbf{E} = -E_0\hat{x} & \text{(R) } \mathbf{B} = B_0\hat{y} \\ \text{(IV) Proton with } \mathbf{v} = 2\frac{E_0}{B_0}\hat{x} & \text{(iv) } \mathbf{E} = E_0\hat{x} & \text{(S) } \mathbf{B} = B_0\hat{z} \\ \hline \end{array}$

Question 1:

In which case would the particle move in a straight line along the negative direction of Y-axis (i.e. move along $- \overset{y}{^}$ )?

In which case will the particle move in a straight line with constant velocity?

In which case will the particle describe a helical path with axis along the positive z-direction?

A uniform magnetic field $B$ exists in the region between $x = 0$ and $x = \frac{3 R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+ Q$ and momentum $p$ directed along $X$ -axis enters region 2 from region 1 at point $P_{1} (y = - R)$ . Which of the following option(s) is/are correct?

* Multiple Correct Options

(A)

When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linear momentum between point

P_{1}

and the farthest point from

Y

-axis is

\frac{p}{2}

(B)

For

B = \frac{8}{13} \frac{p}{QR}

, the particle will enter region 3 through the point

P_{2}

X

-axis.

(C)

For

B > \frac{2}{3} \frac{p}{QR}

, the particle will re-enter region 1.

(D)

For a fixed

B

, particles of same charge

Q

and same velocity

v

, the distance between the point

P_{1}

and the point of re-entry into region 1 is inversely proportional to the mass of the particle.

JEE Advanced 2018

LEVELJEE Advanced

Two infinitely long straight wires lie in the $x y$ -plane along the lines $x = \pm R$ . The wire located at $x = + R$ carries a constant current $I_{1}$ and the wire located at $x = - R$ carries a constant current $I_{2}$ . A circular loop of radius $R$ is suspended with its centre at $(0, 0, 3 R)$ and in a plane parallel to the $x y$ -plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive, if it is in the $+ \hat{j}$ -direction. Which of the following statements regarding the magnetic field $B$ is (are) true?

* Multiple Correct Options

(A)

I_{1} = I_{2}

, then

B

cannot be equal to zero at the origin

(0, 0, 0)

(B)

I_{1} > 0

and

I_{2} < 0

, then

B

can be equal to zero at the origin

(0, 0, 0)

(C)

I_{1} < 0

and

I_{2} > 0

, then

B

can be equal to zero at the origin

(0, 0, 0)

(D)

I_{1} = I_{2}

, then the

z

-component of the magnetic field at the centre of the loop is

(- \frac{μ _{0} I}{2 R})

JEE Advanced 1992

LEVELJEE Advanced

A straight segment $O C$ (of length $L$ ) of a circuit carrying a current $I$ is placed along the $x$ -axis. Two infinitely long straight wires $A$ and $B$ , each extending from $z = - \infty$ to $+ \infty$ , are fixed at $y = - a$ and $y = + a$ respectively, as shown in the figure. If the wires $A$ and $B$ each carry a current $I$ into the plane of the paper, obtain the expression for the force acting on the segment $O C$ . What will be the force on $O C$ if the current in the wire $B$ is reversed?

JEE Advanced 2005

LEVELJEE Advanced

A moving coil galvanometer experiences a torque $= k i$ , where $i$ is current. If $N$ coils of area $A$ each and moment of inertia $I$ is kept in magnetic field $B$ . (2005) (a) Find $k$ in terms of given parameters. (b) If for current $i$ deflection is $\frac{π}{2}$ , find out torsional constant of spring. (c) If a charge $Q$ is passed suddenly through the galvanometer, find out maximum angle of deflection.

JEE Advanced 1998

LEVELJEE Advanced

A particle of mass $m$ and charge $q$ is moving in a region where uniform, constant electric and magnetic fields $E$ and $B$ are present. $E$ and $B$ are parallel to each other. At time $t = 0$ , the velocity $v_{0}$ of the particle is perpendicular to $E$ (Assume that its speed is always $<< c$ , the speed of light in vacuum). Find the velocity $v$ of the particle at time $t$ . You must express your answer in terms of $t$ , $q$ , $m$ , the vector $v_{0}$ , $E$ and $B$ and their magnitudes $v_{0}$ , $E$ and $B$ .

JEE Advanced 2001

LEVELJEE Advanced

A current of 10 A flows around a closed path in a circuit which is in the horizontal plane as shown in the figure. The circuit consists of eight alternating arcs of radii $r_{1} = 0.08$ m and $r_{2} = 0.12$ m. Each subtends the same angle at the centre. (a) Find the magnetic field produced by this circuit at the centre. (b) An infinitely long straight wire carrying a current of 10 A is passing through the centre of the above circuit vertically with the direction of the current being into the plane of the circuit. What is the force acting on the wire at the centre due to the current in the circuit? What is the force acting on the arc $A C$ and the straight segment $C D$ due to the current at the centre?

JEE Main 2012

LEVELJEE Advanced

An infinitely long hollow conducting cylinder with inner radius $R /2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $∣ B ∣$ as a function of the radial distance $r$ from the axis is best represented by

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field $B = (3 \hat{i} + 4 \hat{k}) B_{0}$ exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium. (a) What is the direction of the current I in PQ ? (b) Find the magnetic force on the arm RS. (c) Find the expression for I in terms of $B_{0}$ , a, b and m

JEE Advanced 1998

LEVELJEE Advanced

A uniform constant magnetic field $B$ is directed at an angle of $4 5^{\circ}$ to the $x$ -axis in $x$ - $y$ plane. $P QR S$ is rigid square wire frame carrying a steady current $I_{0}$ , with its centre at the origin $O$ . At time $t = 0$ , the frame is at rest in the position shown in the figure with its sides parallel to $x$ and $y$ -axes. Each side of the frame is of mass $M$ and length $L$ . (1998) (a) What is the magnitude of torque $τ$ acting on the frame due to the magnetic field ? (b) Find the angle by which the frame rotates under the action of this torque in a short interval of time $Δ t$ and the axis about which this rotation occurs ( $Δ t$ is so short that any variation in the torque during this interval may be neglected). Given : the moment of inertia of the frame about an axis through its centre perpendicular to its plane is $\frac{4}{3} M L^{2}$ .

Micro-Topic Strategy Matrix

Biot-Savart Law

Ampere's Circuital Law

Motion of a Charge in Magnetic Fields

Magnetic Force on Current

Magnetic Moment of Current Loop

Moving Coil Galvanometer

Bar Magnet

Magnetic Materials

Chapter Elite-20 Challenge Zone

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } When d≈a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

Comprehension Passage

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In which case would the particle move in a straight line along the negative direction of Y-axis (i.e. move along −y^​)?

In which case will the particle move in a straight line with constant velocity?

In which case will the particle describe a helical path with axis along the positive z-direction?

When $d \approx a$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case

In which case would the particle move in a straight line along the negative direction of Y-axis (i.e. move along $- \overset{y}{^}$ )?