Magnetic Force on Current

Interactive Feed

JEE Advanced 1994

LEVELJEE Advanced

A long horizontal wire $A B$ , which is free to move in a vertical plane and carries a steady current of $20 A$ , is in equilibrium at a height of $0.01 m$ over another parallel long wire $C D$ which is fixed in a horizontal plane and carries a steady current of $30 A$ , as shown in figure. Show that when $A B$ is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

LEVELJEE Advanced

A wire $A B C D E F$ (with each side of length $L$ ) bent as shown in figure and carrying a current $I$ is placed in a uniform magnetic induction $B$ parallel to the positive $y$ -direction. The force experienced by the wire is ......in the ...... direction.

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 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 2015

LEVELJEE Main

A conductor (shown in the figure) carrying constant current $I$ is kept in the $x$ - $y$ plane in a uniform magnetic field $B$ . If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statements is/are

* Multiple Correct Options

(A)

B

is along

\hat{z}

F \propto (L + R)

(B)

B

is along

\hat{x}

F = 0

(C)

B

is along

\hat{y}

F \propto (L + R)

(D)

B

is along

\hat{z}

F = 0

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 2006

LEVELJEE Advanced

Which of the following statement is (are) correct in the given figure ?

* Multiple Correct Options

(A)

Net force on the loop is zero

(B)

Net torque on the loop is zero

(C)

Loop will rotate clockwise about axis

O O^{'}

when seen from

O

(D)

Loop will rotate anticlockwise about

O O^{'}

when seen from

O

JEE Advanced 2010

LEVELJEE Main

A thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

(A)

I B L

(B)

\frac{I B L}{π}

(C)

\frac{I B L}{2 π}

(D)

\frac{I B L}{4 π}

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.

LEVELJEE Main

A rectangular loop carrying a current $i$ is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If steady current $I$ is established in the wire as shown in the figure, the loop will

(A)

rotate about an axis parallel to the wire

(B)

move away from the wire

(C)

move towards the wire

A conducting circular loop of radius $r$ carries a constant current $i$ . It is placed in a uniform magnetic field $B_{0}$ such that $B_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

(A)

i r B_{0}

(B)

2 π i r B_{0}

(C)

zero

(D)

π i r B_{0}

LEVELJEE Main

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

x

-axis

(D)

move towards –ve

x

-axis

JEE Advanced 1986

LEVELJEE Main

Two thin long parallel wires separated by a distance $b$ are carrying a current $i$ ampere each. The magnitude of the force per unit length exerted by one wire on the other is

(A)

\frac{μ _{0} i ^{2}}{b ^{2}}

(B)

\frac{μ _{0} i ^{2}}{2 π b}

(C)

\frac{μ _{0} i}{2 π b}

(D)

\frac{μ _{0} i ^{2}}{2 π b ^{2}}

JEE Main 2015

LEVELJEE Advanced

Two long current carrying thin wires, both with current $I$ , are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $θ$ with the vertical. If wires have mass $λ$ per unit length then, the value of $I$ is ( $g =$ gravitational acceleration)

(A)

sin θ \frac{π λ g L}{μ _{0} c o s θ}

(B)

2 sin θ \frac{π λ g L}{μ _{0} c o s θ}

(C)

2 \frac{π g L}{μ _{0}} tan θ

(D)

\frac{π λ g L}{μ _{0}} tan θ

LEVELJEE Main

If a current is passed through a spring, then the spring will

A square loop of side $2 a$ and carrying current $I$ is kept in xz-plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to Z-axis and passing through point $(0, b, 0)$ , $(b ≫ a)$ . The magnitude of torque on the loop about Z-axis will be

(A)

\frac{2 μ _{0} I ^{2} a ^{2}}{π b}

(B)

\frac{2 μ _{0} I ^{2} a ^{2} b}{π ( a ^{2} + b ^{2} )}

(C)

\frac{μ _{0} I ^{2} a ^{2} b}{2 π ( a ^{2} + b ^{2} )}

(D)

\frac{μ _{0} I ^{2} a ^{2}}{2 π b}

JEE Main 2015

LEVELJEE Main

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $F_{1}$ be the magnetic force on the inner solenoid due to the outer one and $F_{2}$ be the magnetic force on the outer solenoid due to the inner one. Then,

(A)

F_{1} = F_{2} = 0

(B)

F_{1}

is radially inwards and

F_{2}

is radially outwards

(C)

F_{1}

is radially inwards and

F_{2} = 0

(D)

F_{1}

is radially outwards and

F_{2} = 0

LEVELJEE Advanced

Wires 1 and 2 carrying currents $I_{1}$ and $I_{2}$ respectively are inclined at an angle $θ$ to each other. What is the force on a small element $d l$ of wire 2 at a distance $r$ from wire 1 (as shown in figure) due to the magnetic field of wire 1?

(A)

\frac{μ _{0}}{2 π r} I_{1} I_{2} d l tan θ

(B)

\frac{μ _{0}}{2 π r} I_{1} I_{2} d l sin θ

(C)

\frac{μ _{0}}{2 π r} I_{1} I_{2} d l cos θ

(D)

\frac{μ _{0}}{4 π r} I_{1} I_{2} d l sin θ

JEE Main 2014

LEVELJEE Advanced

A conductor lies along the z-axis at $- 1.5 \leq z < 1.5$ m and carries a fixed current of $10.0$ A in $- a_{z}$ direction (see figure). For a field $B = 3.0 \times 1 0^{- 4} e^{- 0.2 x} a_{y}$ T, find the power required to move the conductor at constant speed to $x = 2.0$ m, $y = 0$ in $5 \times 1 0^{- 3}$ s. Assume parallel motion along the x-axis.

Two thin, long, parallel wires, separated by a distance $d$ carry a current of $I$ ampere in the same direction. They will

(A)

attract each other with a force of

\frac{μ _{0} I ^{2}}{( 2 π d )}

(B)

repel each other with a force of

\frac{μ _{0} I ^{2}}{( 2 π d )}

(C)

attract each other with a force of

\frac{μ _{0} I ^{2}}{( 2 π d ^{2} )}

(D)

repel each other with a force of

\frac{μ _{0} I ^{2}}{( 2 π d ^{2} )}

JEE Main 2020

LEVELJEE Advanced

A square loop of side $2 a$ and carrying current $I$ is kept in $x y$ -plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to the $Z$ -axis and passing through the point $(0, b, 0)$ , $(b >> a)$ . The magnitude of the torque on the loop about $Z$ -axis is given by

(A)

\frac{2 μ _{0} I ^{2} a ^{3}}{π b ^{2}}

(B)

\frac{2 μ _{0} I ^{2} a ^{2}}{π b}

(C)

\frac{μ _{0} I ^{2} a ^{3}}{2 π b ^{2}}

(D)

\frac{μ _{0} I ^{2} a ^{2}}{2 π b}

JEE Main 2019

LEVELJEE Advanced

Two wires $A$ and $B$ are carrying currents $I_{1}$ and $I_{2}$ as shown in the figure. The separation between them is $d$ . A third wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from $A$ such that the net force acting on it is zero. The possible values of $x$ are

(A)

x = (\frac{I _{1}}{I _{1} + I _{2}}) d

and

x = (\frac{I _{1}}{I _{1} - I _{2}}) d

(B)

x = (\frac{I _{1}}{I _{1} - I _{2}}) d

and

x = (\frac{I _{2}}{I _{1} + I _{2}}) d

(C)

x = (\frac{I _{2}}{I _{1} + I _{2}}) d

and

x = (\frac{I _{2}}{I _{1} - I _{2}}) d

(D)

x = \pm \frac{I _{1} d}{( I _{1} - I _{2} )}

LEVELJEE Main

Due to the presence of the current $I_{1}$ at the origin in the figure,

(A)

the forces on AB and DC are zero

(B)

the forces on AD and BC are zero

(C)

the magnitude of the net force on the loop is given by

\frac{μ _{0} I I _{1}}{4 π} [2 (b - a) + \frac{π}{3} (a + b)]

(D)

the magnitude of the net force on the loop is given by

\frac{μ _{0} I I _{1}}{24 ab} (b - a)

JEE Main 2021

LEVELJEE Main

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

(A)

Loop assumes circular shape with its plane normal to the field.

(B)

Loop assumes circular shape with its plane parallel to the field.

(C)

Wire gets stretched to become straight.

(D)

Shape of the loop remains unchanged.

LEVELJEE Main

Two long conductors, separated by a distance $d$ carry currents $I_{1}$ and $I_{2}$ in the same direction. They exert a force $F$ on each other. Now, the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3 d$ . The new value of the force between them is

(A)

- 2 F

(B)

\frac{F}{3}

(C)

- \frac{2 F}{3}

(D)

- \frac{F}{3}

Which of the following statement is (are) correct in the given figure ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A conducting loop carrying a current I is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two thin long parallel wires separated by a distance b are carrying a current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is

If a current is passed through a spring, then the spring will

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two thin, long, parallel wires, separated by a distance d carry a current of I ampere in the same direction. They will

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Due to the presence of the current I1​ at the origin in the figure,

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

Two thin long parallel wires separated by a distance $b$ are carrying a current $i$ ampere each. The magnitude of the force per unit length exerted by one wire on the other is

Two thin, long, parallel wires, separated by a distance $d$ carry a current of $I$ ampere in the same direction. They will

Due to the presence of the current $I_{1}$ at the origin in the figure,