Ampere's Law, Cylinders, Solenoid & Toroid

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $i_1 = 10$A, $i_2 = -13$A, $i_3 = 10$A, $i_4 = 7$A, $i_5 = -12$A and $i_6 = 18$ A. The magnetic induction at a perpendicular distance of $10$ cm from the cable is $(\mu_0 = 4\pi \times 10^{-7}$ SI units$)$

Two wires with current 3A and 1.5A are enclosed in a circular loop P. Third parallel wire with current 1A is situated outside the loop as shown. All the wires are perpendicular to the plane of the circular loop. The value of $\oint \vec{B} \cdot \vec{dl}$ around the loop is ($\mu_0 =$ permeability of free space)

The figure given below shows a long straight solid wire of circular cross-section of radius ' $a$ ' carrying steady current $I$. The current $I$ is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field $(B)$ with distance $(r)$ from the axis of the conductor in the region is:

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is:

A. maximum at either ends of the conductor and minimum at the midpoint

B. maximum at the axis of the conductor

C. minimum at the surface of the conductor

D. minimum at the axis of the conductor

E. same at all points in the cross-section of the conductor

Choose the correct answer from the options given below:

The magnitude of the magnetic field inside a long solenoid is increased by

The magnitude of the magnetic field inside a long solenoid is increased by

Choose the WRONG Statement from the following statements.

(A) A toroid is a solenoid bent in the form of a closed ring.

(B) The magnetic field lines of solenoid are straight lines parallel to the axis inside the solenoid. (C) The magnetic field lines of toroid are circular having common centre.

(D) Inside a solenoid, magnetic field may be made strong by passing small current and using laminated coil of soft iron.

A solenoid of 1000 turns is wound uniformly on a glass tube 4 m long and $0.3$ m in diameter. The magnetic intensity at the centre of the solenoid when a current of 4 A flows through it is

A long solenoid carrying a current produces a magnetic field '$B$' along its axis. If the current is tripled and the number of turns per cm is halved then new value of magnetic field will be

The magnetic induction produced inside an ideal solenoid, depends on which of the following quantities?

(a) number of turns per unit length.

(b) radius of the wire.

(c) current flowing throught it.

(d) permeability of the medium.

The magnetic field intensity (H) at the centre of a long solenoid having 'n' turns per unit length and carrying a current I, when no material is kept in it is ($\mu_0$ = permeability of free space)

A long straight wire of a circular cross-section with radius ' a ' carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

The magnetic field intensity H at the centre of a long solenoid having $n$ turns per unit length and carrying a current I, when no material is kept in it is ( $\mu_0 =$ permeability of free space)

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4}\text{ Tesla}$. If the solenoid carries a current of 0.29 A, then the length of the solenoid is _______ $\pi\text{cm}$.

N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A - I_B$, for the given Amperian loops is

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distances ' $\frac{r}{2}$ ' and ' $3r$ ' respectively, from the axis of the wire is

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be:

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is _________.

[Take mass of electron$\mathrm{m_e} = 9 \times 10^{-31}\text{ kg} \quad \frac{\mathrm{N}}{\mathrm{A}^2}, 1\text{ ns} = 10^{-9}\text{ s}]$, charge of electron $|\mathrm{q_e}| = 1.6 \times 10^{-19}\text{ C}, \mu_0 = 4\pi \times 10^{-7}$

A long straight wire of radius $a$ carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from axis of the wire is:

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

A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)$th then the new value of magnetic field will be

The magnetic induction due to an ideal solenoid is independent of

The magnetic field intensity inside current carrying solenoid is $\mathrm{H} = 2.4 \times 10^{3}\text{ A/m}$. If length and number of turns of a solenoid is 15 cm and 60 turns respectively. The current flowing in the solenoid is

A solenoid of length $0.5\text{ m}$ has a radius of $1\text{ cm}$ and is made up of '$\mathrm{m}$' number of turns. It carries a current of $5\text{ A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3}\text{ T}$ then the value of $\mathrm{m}$ is __________.

The magnetic induction along the axis of a toroidal solenoid is independent of

A current of 5 A flows through a toroid having a core of mean radius 20 cm. If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $= 4\pi \times 10^{-7}$ SI units]

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

A long solenoid is formed by winding 70 turns cm${}^{-1}$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($\mu_0 = 4\pi \times 10^{-7}$ TmA ${}^{-1}$)

A rod with circular cross-section area $2\text{ cm}^2$ and length $40\text{ cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4\text{ A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4\pi \times 10^{-6}\text{ Wb}$. The relative permeability of the rod is

(Given: Permeability of vacuum $\mu_0 = 4\pi \times 10^{-7}\text{ NA}^{-2}$)

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be:

A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

Two wires carrying currents $5\text{ A}$ and $2\text{ A}$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3\text{ A}$ is situated outside the loop. The value of $\oint \vec{B}\,\vec{dl}$ around the loop is ( $\mu_0 =$ permeability of free space, $\vec{dl}$ is the length of the element on the Amperion loop)

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by:

A long solenoid carrying current $\mathrm{I}_1$ produces magnetic field $\mathrm{B}_1$ along its axis. If the current is reduced to $20\%$ and number of turns per $\text{cm}$ are increased five times then new magnetic field B${}_2$ is equal to

A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $\text{cm}$ is doubled and the current is made $\left(\frac{1}{3}\right)$rd then the new value of the magnetic field will be

The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a current 'I', when no material is kept in it, is

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is: (permeability of free space = 4$\pi \times$ 10$-$7 H/m)

Figures A and B show 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:

A solenoid 2 m long and 4 cm in diameter has 4 layers of windings of 1000 turns each and carries a current of 5 A. What is the magnetic field at its centre along the axis? [$\mu_0 = 4\pi \times 10^{-7}$ Wb/Am]

A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103 cm3. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0.75 A in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right)$. Find the value of x.

The magnetic field inside a current carrying toroidal solenoid is $0.2\text{ mT}$. What is the magnetic field inside the toroid if the current through it is tripled and radius is made $\frac{1}{3}$rd?

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current i0, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b?

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3T, the field at the center of C would be: (Assume that the magnetic field is confined with in the volume of respective solenoid).

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and 2$a$, respectively from the axis of the wire is:

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is:

$\left(\mu_0 = 4\pi \times 10^{-7}\, TmA^{-1}\right)$

An iron rod of volume 10–3 m3 and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be:

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1 = +10\text{ A}, I_2 = -13\text{ A}, I_3 = +10\text{ A}, I_4 = +7\text{ A}, I_5 = -12\text{ A}$ and $I_6 = +18\text{ A}$. The magnetic induction at a perpendicular distance of 10 cm from the cable is

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

A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor, is correctly represented by the figure:

Two toroids 1 and 2 have total no. of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current $i$, the ratio of the magnetic fields along the two loops is,

A long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance $\frac{a}{2}$ and 2$a$ respectively, from the axis of the wire is

A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization $\vec{M}$ (magnetic moment/volume), then $\overrightarrow{|M|}$ is:

A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R.$ The magnitude of the magnetic induction along its axis is:

A long straight wire of radius $a$ carries a steady current $i.$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $a/2$ and $2a$ is

A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then

A long solenoid has $200$ turns per $cm$ and carries a current $i.$ The magnetic field at its center is $6.28 \times 10^{-2}\ Weber/m^2.$ Another long solenoid has $100$ turns per $cm$ and it carries a current $\frac{i}{3}$. The value of the magnetic field at its center is

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of the magnetic field is

If a long hollow copper pipe carries a current, then magnetic field is produced