Force on Current-Carrying Conductors

A wire carrying current 'I' along x axis has length 'L' and it is kept in a magnetic field $B(\hat{i} + 2\hat{j} - 2\hat{k})$ T. The magnitude of magnetic force acting on the wire is

The currents through two thin long parallel wires, A and B carrying $I$ and $\frac{I}{3}$ respectively, in the same direction. The distance between two wires is '$d$'. The magnitude of force per unit length exerted by wire A on wire B is

Two thin long parallel wires, $W_1$ and $W_2$ separated by distance '$a$', carry currents $i$ and $3i$ respectively in the same direction. The magnitude of the force per unit length exerted by wire $W_1$ on wire $W_2$ is

Two long straight wires are arranged parallel to each other and are kept $20$ cm apart in vacuum. They carry currents of $2$ A and $4$ A respectively in the same direction. What will be the magnetic force on a length of $10$ cm of either wire?

($\mu_0 = 4\pi \times 10^{-7}$ SI units)

Three long straight parallel wires carrying currents are arranged as shown. The wire C carries a current $50$ A is so placed that it experiences no force. The distance of wire C from wire A in cm is

A wire AB is carrying steady current $I_1$ and is kept on the table. Another wire CD carrying current $I_2$ is held directly above as shown in figure. When the wire CD is left free and it remains suspended at its position, its mass per unit length is (g=acceleration due to gravity, $\mu_0$ = permeability of free space)

Two infinitely long parallel conducting wires $A$ and $B$ carry currents $I$ and $2I$, respectively, in the same direction. The wire $A$ has uniform mass per unit length $\lambda$ and lies on an insulated floor. The wire $B$ is kept fixed at a height $h$ above the floor. The minimum magnitude of $h$ so that the wire $A$ does not rise from the floor is: [ $g$ is the acceleration due to gravity and $\mu_0$ is the permeability of free space.]

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire $Q$ is ______.

$\left(\mu_0 = 4\pi \times 10^{-7}\text{ T m/A}\right)$

A square loop ABCD of side L carrying a current $I_1$ is placed at a distance $(L/3)$ from a conductor coplaner with a straight conductor XY carrying current $I_2$ as shown in figure. The net force on the loop will be ($\mu_0$ = magnetic permeability)

A wire of length $L$ carries current $I$ along x - axis. A magnetic field $\vec{B} = B_0(\hat{i} - \hat{j} - \hat{k})\text{ T}$ acts on the wire. The magnitude of magnetic force acting on the wire is

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ________mN.

Two long straight wires A and B carrying equal current 'I' were kept parallel to each other at distance ' $d$ ' apart. Magnitude of magnetic force experienced by length $L$ of wire $A$ is ' $F$ '. If the distance between the wires is made half and currents are doubled, force $F_2$ on length $L$ of wire $A$ will be

Two long conductors separated by a distance ' d ' carry currents ' $I_1$ ' and ' $I_2$ ' in the same directions. They exert a force ' $F$ ' on each other. The distance between them is increased to ' 3 d '. If new repulsive force of magnitude ' $\frac{2}{3}F$ ' is found between these conductors, the required change in the magnitude and direction of one of the currents in the conductor is respectively [length of the conductors is constant]

A square coil ABCD of side ' L ' is carrying a current in clockwise direction. A straight conductor carrying current $I_2$ (upward direction) is kept parallel to side AB at a distance $\frac{L}{3}$ in the plane of $ABCD$. The net force on the coil ABCD is ( $\mu_0 =$ magnetic permeability)

Two parallel wires separated by distance 'b' are carrying equal current ' $I$ ' in the same direction. The force per unit length of the wire 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 __________ $\times 10^{-6}\text{ N/m}$.

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

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

The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x)\hat{k}$. A square loop of edge $50\text{ cm}$ carrying 0.5 A current is placed in $x\text{-}y$ plane with its edges parallel to the $x\text{-}y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ $\text{mN}$.

A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a uniform magnetic field ' B ' directed outwards in the shaded region. A d.c. voltage ' V ' is applied to the loop. For what value of ' $V$ ' the magnetic force will exactly balance the weight of the supporting mass ' M '? (side of loop = L, $g =$ acceleration due to gravity)

A 2A 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, $g = 10\text{ m/s}^2$).

Three infinite straight wires $A, B$ and C carry currents as shown in figure. The resultant force on wire $B$ is directed

Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a current of 5.0 A is so placed that it experiences no force. The distance of wire C from wire $D$ is

A wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 4\hat{k})\text{ T}$. The magnitude of the magnetic force acting on the wire is:

A long straight wire of length $2\text{ m}$ and mass $250\text{ g}$ is suspended horizontally in a uniform horizontal magnetic field of $0.7\text{ T}$. The amount of current flowing through the wire will be $\left(g = 9.8\text{ m s}^{-2}\right)$:

A straight wire $AB$ of mass $40\text{ g}$ and length $50\text{ cm}$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40\text{ T}$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ___________ A.

$($ Take $g = 10\text{ m s}^{-2}$ ).

Two wires $2\text{ mm}$ apart supply current to a $100\text{ V},\ 1\text{ kW}$ heater. The force per metre between the wires is ( $\mu_0 = 4\pi \times 10^{-7}$ SI unit)

10 A current is flowing in two straight parallel wires in the same direction. Force of attraction between them is $1 \times 10^{-3}\text{ N}$. If the current is doubled in both the wires the force will be

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 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 cm length of wire P will be:

A single turn current loop in the shape of a right angle triangle with side $5\text{ cm},\ 12\text{ cm},\ 13\text{ cm}$ 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 on the $5\text{ cm}$ side will be $\frac{x}{130}\text{ N}$. The value of '$x$' is

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

A massless square loop, of wire of resistance $10\ \Omega$, supporting a mass of $1\text{ g}$, hangs vertically with one of its sides in a uniform magnetic field of $10^{3}\text{ G}$, directed outwards in the shaded region. A dc voltage $\text{V}$ is applied to the loop. For what value of $\text{V}$, the magnetic force will exactly balance the weight of the supporting mass of $1\text{ g}$?

(If sides of the loop $= 10\text{ cm},\ g = 10\text{ m s}^{-2}$)

$A, B$ and $C$ are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance $AB$ and $BC$ is same as '$d$'. If '$F_1$' is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $C$ on $A$, then

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 between them is also increased to $3d$. The new value of force between them is

A long straight wire carrying a current of $25\text{ A}$ rests on the table. Another wire PQ of length $1\text{ m}$ and mass $2.5\text{ g}$ carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will wire PQ rise? ($\mu_0 = 4\pi \times 10^{-7}$ SI unit)

A current carrying rectangular loop PQRS is made of uniform wire. The length $PR = QS = 5\text{ cm}$ and $PQ = RS = 100\text{ cm}$. If ammeter current reading changes from I to $2I$, the ratio of magnetic forces per unit length on the wire $PQ$ due to wire $RS$ in the two cases respectively $\left(f_{PQ}^{I} : f_{PQ}^{2I}\right)$ is:

Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is: ($\mu$0 = 4$\pi \times$ 10$-$7 SI unit)

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $\times$ 10$-$6 N, then the value of x is approximately:

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10$-$5 N, then separation between the wires is ____________ cm.

A triangular shaped wire carrying $10\text{ A}$ current is placed in a uniform magnetic field of $0.5\text{ T}$, as shown in figure. The magnetic force on segment $CD$ is

(Given $BC = CD = BD = 5\text{ cm}$.)

As shown in the figure, a metallic rod of linear density $0.45\text{ kg m}^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $45^\circ$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15\text{ T}$ magnetic field is acting on it in the vertical upward direction, will be:

{Use $g = 10\text{ m/s}^2$}

A wire X of length $50\text{ cm}$ carrying a current of $2\text{ A}$ is placed parallel to a long wire $Y$ of length $5\text{ m}$. The wire $Y$ carries a current of $3\text{ A}$. The distance between two wires is $5\text{ cm}$ and currents flow in the same direction. The force acting on the wire $Y$ is

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.

Two long conductors, separated by a distance '$d$' carry currents '$I_1$' and '$I_2$ ' in the same directions. 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 '$3d$'. The new value of the force between them is

A, B and C are three parallel conductors of equal lengths carrying currents $I, I$ and $2I$ respectively. Distance between A and B is '$x$' and that between B and C is also '$x$'. $F_1$ is the force exerted by conductor $B$ on $A.\ F_2$ is the force exerted by conductor $C$ on $A$. Current $I$ in $A$ and $I$ in $B$ are in same direction and current $2I$ in $C$ is in opposite direction. Then

Two parallel conductors carrying unequal currents in the same direction ............

Two wires A & B are carrying currents I1 & I2 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 rigid square loop of side 'a' and carrying current I2 is lying on a horizontal surface near a long current I1 carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be:

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop applies a force F on the wire then:

A metallic rod of mass per unit length 0.5 kg m–1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $\text{'}I\text{'}$ along the same direction as shown in figure. Magnitude of force per unit length on the middle wire $\text{'}B\text{'}$ is given by

A square loop ABCD carrying a current $i$, is placed near and coplanar with a long straight conductor XY carrying a current $I$, the net force on the loop will be

Two long straight parallel wires, carrying (adjustable) currents I1 and I2, are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product I1I2, would be:

A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle 2$\theta$0 at the center of the circle (of which it forms an arch) then the tension in the wire is:

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 $\text{'}\theta\text{'}$ with the vertical. If wires have mass $\lambda$ per unit-length then the value of $I$ is:

($g =$ gravitational acceleration)

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

A conductor lies along the $z$-axis at $-1.5 \le z < 1.5\text{ m}$ and carries a fixed current of $10.0\text{ A}$ in $-\hat{a}_z$ direction (see figure). For a field $\vec{B} = 3.0 \times 10^{-4}\, e^{-0.2x}\, \hat{a}_y\text{ T},$ find the power required to move the conductor at constant speed to $x = 2.0\text{ m},\ y = 0\text{ m}$ in $5 \times 10^{-3}\text{ s}.$ Assume parallel motion along the $x$-axis.

A circular coil ABCD carrying a current 'i' is placed in a uniform magnetic field. If the magnetic force on the segment AB is $\vec{F}$, the force on the remaining segment BCDA is

A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic field $\vec{B}$ pointing into 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:

One of the two small circular coils, (none of them having any self-inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a dc supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?

A square loop, carrying a steady current $I$, is placed in a horizontal plane near a long straight conductor carrying a steady current $I$1 at a distance d from the conductor as shown in figure. The loop will experience

A current carrying closed loop in the form of a right angle isosceles triangle ABC is placed in uniform magnetic field acting along AB. If the magnetic force on the arm BC is $\vec{F},$ the force on the arm AC is

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\vec{F}$, the net force on the remaining three arms of the loop is

A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $= a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^\circ.$ Another straight thin wire steady current $I_1$ flowing out of the plane of the paper is kept at the origin.

Due to the presence of the current $I_1$ at the origin:

A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are F1, F2 and F3 respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

Two thin, long, parallel wires, separated by a distance $'d'$ carry a current of $'i'\ A$ in the same direction. They will

Two long conductors, separated by a distance $d$ carry current $I_1$ 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 $3d$. The new value of the force between them is

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

Wires $1$ and $2$ carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?

Two long parallel wires are at a distance of $1\text{ m}$. Both of them carry one ampere of current. The force of attraction per unit length between the two wires is

Two parallel wires in free space are $10\text{ cm}$ apart and each carries a current of $10\text{ A}$ in the same direction. The force exerted by one wire on the other, per metre length is

A straight wire of length $0.5$ metre and carrying a current of $1.2$ ampere is placed in uniform magnetic field of induction $2$ tesla. The magnetic field is perpendicular to the length of the wire. The force on the wire is