Force on a Current Element

Q. An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57\times {10}^{–2}T$. If the value of $\frac{e}{m}$ is $1.76\times {10}^{11}C/kg$, the frequency of revolution of the electron is

1. $62.8MHz$
2. $6.28MHz$
3. $1GHz$
4. $100MHz$

Q. A conductor of $3\text{m}$ length, is moving with a speed of ${10}^2\text{m/s}$. It is moving in a direction, perpendicular to its length, as well as to a magnetic field of ${10}^{-3}\text{T}$. The force required to move it with this constant speed is -

1. $0.3\text{N}$
2. $0.9\text{N}$
3. $0$
4. $3\times {10}^{-3}\text{N}$

Q. The magnetic field at the centre of a circular coil of radius r is $\pi$ times that due to a long straight wire at a distance r from it, for equal currents. Figure here shows three cases : in all cases the circular part has radius r and straight ones are infinitely long. For same current the B field at the centre P in cases 1, 2, 3 have the ratio

1. $(-\frac{\pi }{2}):\left(\frac{\pi }{2}\right):(\frac{3\pi }{4}-\frac{1}{2})$
   
2. $(-\frac{\pi }{2}+1):(\frac{\pi }{2}+1):(\frac{3\pi }{4}-\frac{1}{2})$
   
3. $-\frac{\pi }{2}:\frac{\pi }{2}:3\frac{\pi }{4}$
   
4. $(-\frac{\pi }{2}-1):(\frac{\pi }{2}-\frac{1}{4}):(\frac{3\pi }{4}-\frac{1}{2})$

Q. 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

1. Contract
2. Expand
3. Move towards +ve x -axis
4. Move towards –ve x-axis

Q. A copper disc of radius $0.1\text{m}$ is rotated about its centre at $20$ revolutions per second in a uniform magnetic field of $0.1\text{T}$ with its plane perpendicular to the field. The emf induced across the radius of the disc is -

1. $\frac{\pi }{20}\text{V}$
2. $\frac{\pi }{10}\text{V}$
3. $20\pi \text{mV}$
4. $100\pi \text{mV}$

Q. A particle with charge q and mass m is projected with kinetic energy K into the region between two plates of a uniform magnetic field B as shown below.

If the particle is to miss collision with the opposite plate, the maximum value of B is

1. $\frac{\sqrt{2Kq}}{md}$
2. $\frac{\sqrt{2K}}{qmd}$
3. $\frac{\sqrt{2Kd}}{qm}$
4. $\frac{\sqrt{2Km}}{qd}$

Q. A long, thin-walled pipe of radius R carries a current I along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the centre of the pipe due to quarter portion of the pipe is

1. None
2. $\frac{{\mu }_{0}I\sqrt{2}}{4{\pi }^{2}R}$
3. $\frac{{\mu }_{0}I}{{\pi }^{2}R}$
4. $\frac{2{\mu }_{0}I\sqrt{2}}{{\pi }^{2}R}$

Q. A current of $1.5A$ is flowing through a triangle, of side $9\text{cm}$ each. The magnetic field at the centroid of the triangle is
(Assume that the current is flowing in the clockwise direction.)

1. $2\sqrt{3}\times {10}^{-7}\text{T},\text{outside the plane of triangle}$
2. $2\sqrt{3}\times {10}^{-5}\text{T},\text{inside the plane of triangle}$
3. $3\times {10}^{-5}\text{T},\text{inside the plane of triangle}$
4. $3\times {10}^{-7}\text{T},\text{outside the plane of triangle}$

Q. 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 the distance of its centre from the wire is $d(d>>a)$. If the loop applies a force $F$ on the wire, then:

1. $F\propto \left(\frac{a^2}{d^3}\right)$
2. $F=0$
3. $F\propto \left(\frac{a}{d}\right)$
4. $F\propto {\left(\frac{a}{d}\right)}^2$

Q. A circular wire $\text{ABC}$ and a straight conductor $\text{ADC}$ are assumed to be a carrying current $i$ and are kept in the magnetic field $B$ then considering points $\text{A}$ and $\text{C}$ as shown in the figure.

1. Force on $\text{ABC}$ is more than that on $\text{ADC}$
2. Force on $\text{ABC}$ is less than that on $\text{ADC}$
3. Force on $\text{ABC}$ is equal to that on $\text{ADC}$
4. Cannot be predicted with the given data

Q.
As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius 'r' concentrically inside a square of side 'a', where a: r = 8 : $\pi$. A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre O.

1. $\frac{{\mu }_{0}I}{2\pi a}\sqrt{2}(\sqrt{2}-1)$
2. $\frac{{\mu }_{0}I}{2\pi a}(\sqrt{2}+1)$
3. $\frac{{\mu }_{0}I}{\pi a}2\sqrt{2}(\sqrt{2}+1)$
4. $\frac{{\mu }_{0}I}{\pi a}2\sqrt{2}(\sqrt{2}-1)$

Q. The figure shows a uniform magnetic field $B$ confined to a cylindrical volume and is increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at $\text{P}$ is

1. $\text{zero}$
2. $\text{towards right}$
3. $\text{towards left}$
4. $\text{upwards}$

Q. Two concentric rings, one of radius R and total charge +Q and the second of radius 2R and total charge $-\sqrt{8}Q$, lie in x - y plane (i.e. z = 0 plane). The common centre of rings lies at origin and the common axis coincides with the z-axis. The charge is uniformly distributed on both rings. At a distance $(x{)}^{y}R$ from origin the net electric field on z-axis zero. Find xy

Q. A loop carrying current $I$ lies in the $xy$-plane as shown in figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic field $B=B_0\hat{i}$ exists where $B_0$ is a constant. The torque acting on the current loop is:

1. $B_{0}I{a}^2(1+\frac{\pi }{2})\hat{j}$
2. $B_{0}I{a}^2\pi \hat{j}$
3. $-B_{0}I{a}^2\pi \hat{k}$
4. $B_{0}I{a}^2(1+\frac{3\pi }{2})\hat{i}$

Q. Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases, which type of force acts between the two wires

1. Repulsion force in both cases
2. Attraction force when in parallel and repulsion force when in series
3. Repulsion force when in parallel and attraction force when in series
4. Attraction force in both cases

Q. What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field ${}^{\prime }{B}^{\prime }$ at origin: -

1. $4B$
2. $\sqrt{2}B$
3. $2\sqrt{2}B$
4. Zero

Q. An elastic circular wire of length l carries a current I. It is placed in a uniform magnetic field $\overrightarrow{B}$ (Out of paper) such that its plane is perpendicular to the direction of $\overrightarrow{B}$. The wire will experience

1. No force
2. A torque
3. A stretching force
4. A compressive force

Q. A hollow cylinder having infinite length and carrying uniform current per unit length $\lambda$ along the circumference as shown in the figure.


Magnetic field inside the cylinder is

1. $\frac{{\mu }_0\lambda }{2}$
2. ${\mu }_0\lambda$
3. $2{\mu }_0\lambda$
4. None

Q. $A,B$ and $C$ are parallel conductors of equal lengths carrying currents $i$ and $2i$ respectively. Distance between $A$ and $B$ is $x$. Distance between $B$ and $C$ is also $x$. $F_1$ is the force exerted by $B$ on $A$. $F_2$ is the force exerted by $C$ on $A$. Choose the correct relation among the following.

1. $|{\overrightarrow{F}}_1|=2|{\overrightarrow{F}}_2|$
2. $|{\overrightarrow{F}}_2|=2|{\overrightarrow{F}}_1|$
3. $|{\overrightarrow{F}}_1|=3|{\overrightarrow{F}}_2|$
4. $|{\overrightarrow{F}}_1|=|{\overrightarrow{F}}_2|$

Q.

A circular loop of radius a, carrying a current i, is placed in a two - dimensional magnetic field. the centre of the loop coincides with the centre of the field (figure 34 - E4). The strength of the magnetic field at the periphery of the loop is B. Find the magnetic force on the wire.

Q. Three long parallel straight conductors A, B and C carrying currents 3A, 1A and 2A respectively. The force experienced by the conductor ‘B’ of length 0.5 m is

1. $10\times {10}^{-6}N$ from right to left
2. $10\times {10}^{-6}N$ from left to right
3. $5\times {10}^{-6}N$ from right to left
4. $5\times {10}^{-6}N$ from left to right

Q. A proton and an $\alpha -$ particle enter the same magnetic field which is perpendicular to their velocity. If both particles have same kinetic energy, then the ratio of their radii of the circular path is

1. $1:1$
2. $1:2$
3. $2:1$
4. $1:4$

Q.

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

1. 
   if $\overrightarrow{B}$ is along $\hat{z},F\propto (L+R)$
2. 
   if $\overrightarrow{B}$ is along $\hat{x},F=0$
3. 
   if $\overrightarrow{B}$ is along $\hat{y},F\propto (L+R)$
4. 
   if $\overrightarrow{B}$ is along $\hat{z},F=0$

Q. The figure shows a square loop, each side of $10\text{cm}$ in the $xy-$plane, with its centre at the origin. An infinite wire is at $z=12\text{cm}$ above $y-$axis. If the torque on loop due to magnetic force is expressed as $x\times {10}^{-7}\text{N-m}$, fill the value of $x$.

Q. The force between two parallel conductors, each of length $50\text{m}$ and distance $20\text{cm}$ apart, is ${10}^{-2}\text{N}$. If the current in one conductor is double to that in another one, then their values will respectively be

1. $10\text{A}$ and $20\text{A}$
2. $50\text{A}$ and $100\text{A}$
3. $5\text{A}$ and $10\text{A}$
4. $25\text{A}$ and $50\text{A}$

Q. A wire of length $l$ carries a current $I$ along $\text{x-}$axis. A magnetic field exists which is given as $\overrightarrow{B}=B_0(\hat{i}+\hat{j}+\hat{k})\text{T}$. The magnitude of the magnetic force acting on the wire will be

1. $B_{0}Il$
2. $B_{0}Il\sqrt{2}$
3. $2B_{0}Il$
4. $\frac{B_{0}Il}{\sqrt{2}}$

Q. A conducting rod $\text{PQ}$ of length $5\text{m}$ oriented as shown in figure is moving with velocity $2\hat{i}{\text{ms}}^{-1}$ without any rotation in a uniform magnetic field $(3\hat{j}+4\hat{k})\text{T}.$ The emf induced in the rod is

1. $36\text{V}$
2. $34\text{V}$
3. $32\text{V}$
4. $38\text{V}$

Q. A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x}\times {10}^{-5}Nm$. The value of x is .

Q. A straight wire carrying a current $i_1$ runs along the axis of a circular current $i_2$. Then the force of interaction between the two current carrying conductors is

1. $\infty$
2. Zero
3. $\frac{{\mu }_0}{4\pi }\frac{2i_1{i}_2}{r}$
4. $\frac{2i_1{i}_2}{r}\frac{N}{m}$

Q. A rigid square of loop of side $a$ and carrying current $I_2$ is lying on a horizontal surface near a long current $I_1$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be

1. Repulsive and equal to $\frac{{\mu }_0{I}_1{I}_2}{2\pi }$
2. Zero
3. Repulsive and equal to $\frac{{\mu }_0{I}_1{I}_2}{4\pi }$
4. Attractive and equal to $\frac{{\mu }_0{I}_1{I}_2}{3\pi }$