Ampere's Circuital Law

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JEE Advanced 2013

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$ . This cylinder is placed coaxially inside an infinite solenoid of radius $2 R$ . The solenoid has $n$ turns per unit length and carries a steady current $I$ . Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)

0 < r < R

, the magnetic field is non-zero

(B)

In the region

R < r < 2 R

, the magnetic field is along the common axis

(C)

In the region

R < r < 2 R

, the magnetic field is tangential to the circle of radius

r

, centered on the axis

(D)

In the region

r > 2 R

, the magnetic field is non-zero

JEE Main 2000

LEVELJEE Main

Two long parallel wires are at a distance $2 d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $X X^{'}$ is given by

Two long straight parallel wires are $2 m$ apart, perpendicular to the plane of the paper. The wire $A$ carries a current of $9.6 A$ , directed into the plane of the paper. The wire $B$ carries a current such that the magnetic field of induction at the point $P$ , at a distance of $10/11 m$ from the wire $B$ , is zero. Find (a) the magnitude and direction of the current in $B$ . (b) the magnitude of the magnetic field of induction at the point $S$ . (c) the force per unit length on the wire $B$ .

JEE Advanced 2012

LEVELJEE Advanced

A cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2 a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12} μ_{0} a J$ , then the value of $N$ is

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

An infinitely long wire, located on the z-axis, carries a current $I$ along the $+ z$ -direction and produces the magnetic field $B$ . The magnitude of the line integral $\int B \cdot d l$ along a straight line from the point $(- 3 a, a, 0)$ to $(a, a, 0)$ is given by [ $μ_{0}$ is the magnetic permeability of free space.]

(A)

7 μ_{0} I /24

(B)

7 μ_{0} I /12

(C)

μ_{0} I /8

(D)

μ_{0} I /6

JEE Main 2020

LEVELJEE Main

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)

\frac{3}{2}

(B)

2

(C)

\frac{2}{3}

(D)

\frac{1}{2}

LEVELJEE Advanced

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)

\frac{μ _{0} I}{2 π ^{2} R}

(B)

\frac{μ _{0} I}{2 π R}

(C)

\frac{μ _{0} I}{4 π R}

(D)

\frac{μ _{0} I}{π ^{2} R}

JEE Main 2021

LEVELJEE Main

Figures A and B shown 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

Two very long, straight and insulated wires are kept at $9 0^{\circ}$ angle from each other in $x y$ -plane as shown in the figure. These wires carry currents of equal magnitude $I$ , whose directions are shown in the figure. The net magnetic field at point P will be

(A)

zero

(B)

+ \frac{μ _{0} I}{π d} (\overset{z}{^})

(C)

- \frac{μ _{0} I}{2 π d} (\overset{x}{^} + \overset{y}{^})

(D)

\frac{μ _{0} I}{2 π d} (\overset{x}{^} + \overset{y}{^})

LEVELJEE Main

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 $2 a$ is

A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from East to West. The magnetic field directly below it on the ground is (take $μ_{0} = 4 π \times 1 0^{- 7} T m A^{- 1}$ )

(A)

2.5 \times 1 0^{- 7} T

, Southward

(B)

5 \times 1 0^{- 6} T

, Northward

(C)

5 \times 1 0^{- 6} T

, Southward

(D)

2.5 \times 1 0^{- 7} T

, Northward

LEVELJEE Main

A long solenoid has $200$ turns per cm and carries a current $I$ . The magnetic field at its centre is $6.28 \times 1 0^{- 2} Wb/m^{2}$ . Another long solenoid has $100$ turns per cm and it carries a current $I /3$ . The value of the magnetic field at its centre is

(A)

1.05 \times 1 0^{- 2} Wb/m^{2}

(B)

1.05 \times 1 0^{- 5} Wb/m^{2}

(C)

1.05 \times 1 0^{- 3} Wb/m^{2}

(D)

1.05 \times 1 0^{- 4} Wb/m^{2}

JEE Main 2021

LEVELJEE Main

A solenoid of $1000$ turns per metre has a core with relative permeability $500$ . Insulated windings of the solenoid carry an electric current of $5 A$ . The magnetic flux density produced by the solenoid is (Permeability of free space $= 4 π \times 1 0^{- 7} H/m$ )

(A)

π T

(B)

2 \times 1 0^{- 3} π T

(C)

\frac{π}{5} T

(D)

1 0^{- 4} π T

LEVELJEE Main

Two long parallel wires are at a distance $2 d$ apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line $x x^{'}$ is given by

A co-axial 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 $i_{0}$ , 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) $a < x < b$ ?

(A)

\frac{x ^{2}}{a ^{2}}

(B)

\frac{a ^{2}}{x ^{2}}

(C)

\frac{x ^{2}}{b ^{2} - a ^{2}}

(D)

\frac{b ^{2} - a ^{2}}{x ^{2}}

JEE Main 2021

LEVELJEE Main

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 centre of A is 3T, the field at the centre of C would be (Assume that, the magnetic field is confined with in the volume of respective solenoid)

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

(A)

the magnetic field is zero only on the axis of the pipe

(B)

the magnetic field is different at different points inside the pipe

(C)

the magnetic field at any point inside the pipe is zero

(D)

the magnetic field at all points inside the pipe is the same but not zero

LEVELJEE Main

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

\frac{μ _{0}}{4 π} \cdot \frac{2 I}{r}

(D)

\frac{2 I}{r}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

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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 centre of A is 3T, the field at the centre of C would be (Assume that, the magnetic field is confined with in the volume of respective solenoid)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A current I flows along the length of an infinitely long, straight, thin walled pipe. Then,

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 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 $\frac{a}{2}$ and $2 a$ is

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

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