Source And Effects Of Magnetic Field | Physics JEE previous year questions with Solutions

Q 1 :

Two insulated circular loops A and B of radius 'a' carrying a current of 'I' in the anti-clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be ______. [2024]

$\frac{\sqrt{2} μ_{0} I}{2 a}$
$\frac{μ_{0} I}{2 a}$
$\frac{\sqrt{2} μ_{0} I}{a}$
$\frac{2 μ_{0} I}{a}$

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(1)

${\vec{B}}_{A} = \frac{μ_{0} I}{2 a}$

${\vec{B}}_{B} = \frac{μ_{0} I}{2 a}$ $∵$ ${\vec{B}}_{net} = \frac{\sqrt{2} μ_{0} I}{2 a}$

Q 2 :

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_{1} = 2 π m$ and $R_{2} = 4 π m$ , carrying current $I = 4 A$ as per figure given below is $α \times 10^{- 7} T$ . The value of $α$ is ______. (Centre O is common for all segments) [2024]

(3)

$\frac{μ_{0} i}{2 R_{2}} (\frac{π}{2 π}) \otimes + \frac{μ_{0} i}{2 R_{1}} (\frac{π}{2 π}) \otimes$

$(\frac{μ_{0} i}{4 R_{2}} + \frac{μ_{0} i}{4 R_{1}}) \otimes$

$\frac{4 π \times 10^{- 7} \times 4}{4 \times 4 π} + \frac{4 π \times 10^{- 7} \times 4}{4 \times 2 π}$

$= 3 \times 10^{- 7} = α \times 10^{- 7}$

$α = 3$

Q 3 :

Two circular coils P and Q of 100 turns each have same radius of $π$ cm. The currents in P and R are 1A and 2A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x} m T,$ where $x =$ ____ .

$[Use μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1}]$ [2024]

(20)

$B_{P} = \frac{μ_{0} N i_{1}}{2 r} = \frac{μ_{0} \times 1 \times 100}{2 π} = 2 \times 10^{- 3} T$

$B_{Q} = \frac{μ_{0} N i_{2}}{2 r} = \frac{μ_{0} \times 2 \times 100}{2 π} = 4 \times 10^{- 3} T$

$B_{net} = \sqrt{B_{P}^{2} + B_{Q}^{2}} = \sqrt{20} mT$

$x = 20$

Q 4 :

An infinite wire has a circular bend of radius a, and carrying a current $I$ as shown in figure.

The magnitude of magnetic field at the origin O of the arc is given by: [2025]

$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{π}{2} + 1]$
$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{3 π}{2} + 1]$
$\frac{μ_{0}}{2 π} \frac{I}{a} [\frac{π}{2} + 2]$
$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{3 π}{2} + 2]$

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(2)

$B_{1} = \frac{μ_{0} I}{4 π a} \otimes$

$B_{2} = \frac{μ_{0}}{4 π} \frac{I}{a} (\frac{3 π}{2}) \otimes$

$B_{3} = 0$

$B = \frac{μ_{0}}{4 π} \frac{I}{a} (1 + \frac{3 π}{2}) \otimes$

Q 5 :

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 [2025]

$[\frac{a}{4}, \frac{a}{2}]$
$[\frac{a}{2}, 2 a]$
$[\frac{a}{2}, 3 a]$
$[\frac{a}{4}, 2 a]$

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(2)

Maximum possible magnetic field on the surface

$B_{\max} = \frac{μ_{0} I}{2 π a} \Rightarrow \frac{B_{\max}}{2} = \frac{μ_{0} I}{4 π a}$

It can be obtained inside as well as outside the wire.

For inside, $\frac{μ_{0} I}{4 π a} = \frac{μ_{0} I r}{2 π a^{2}} \Rightarrow r = \frac{a}{2}$

For outside, $\frac{μ_{0} I}{4 π a} = \frac{μ_{0} I}{2 π r} \Rightarrow r = 2 a$

Correct answer $[\frac{a}{2}, 2 a]$

Q 6 :

Let $B_{1}$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current $I$ . Let $B_{2}$ be the magnitude of magnetic field at an axial distance 'x' from the centre. For $x : R = 3 : 4, \frac{B_{2}}{B_{1}}$ is: [2025]

4 : 5
16 : 25
64 : 125
25 : 16

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(3)

The magnitude of magnetic field at centre of a circular coil, $B_{1} = \frac{μ_{0} i}{2 R}$

The magnitude of magnetic field at an axial distance $x = \frac{3 R}{4}$ from the centre.

$B_{2} = \frac{μ_{0} i R^{2}}{2 {(R^{2} + x^{2})}^{3 / 2}} = \frac{μ_{0} i R^{2}}{2 {(\frac{5 R}{4})}^{3}} = \frac{64}{125} (\frac{μ_{0} i}{2 R})$

$\Rightarrow \frac{B_{2}}{B_{1}} = \frac{64}{125}$

Q 7 :

A loop ABCDA, carrying current $I$ = 12A, is placed in a plane, consists of two semi-circular segments of radius $R_{1} = 6 π m$ and $R_{2} = 4 π m$ . The magnitude of the resultant magnetic field at center O is $k \times 10^{- 7} T$ . The value of k is _______ (Given $μ_{0} = 4 π \times 10^{- 7} T {mA}^{- 1}$ ) [2025]

(1)

Magnetic field due to AB and CD = 0

$B = \frac{μ_{0} I}{2 r} (\frac{θ}{2 π})$ for an arc

For semi-circule $B = \frac{μ_{0} I}{4 r}$

$B_{net} = \frac{μ_{0} I}{4 {4 π}} - \frac{μ_{0} I}{4 {6 π}}$

$= \frac{μ_{0} I}{4 π} {\frac{1}{4} - \frac{1}{6}}$

$= 10^{- 7} \times 12 \times \frac{2}{24} = 10^{- 7} T \Rightarrow k = 1$

Q 8 :

Match the Column – I with Column – II: [2023]

Choose the correct answer from the options given below:

A – I; B – III; C – IV; D – II
A – III; B – IV; C – I; D – II
A – II; B – I; C – IV; D – III
A – III; B – I; C – IV; D – II

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(4)

$A \to B_{0} = \frac{μ_{0}}{4 π} \frac{i}{r} ⊙ + \frac{μ_{0} i}{2 r} \otimes + \frac{μ_{0}}{4 π} \frac{i}{r} ⊙$

$= \frac{μ_{0}}{2 π} \frac{i}{r} ⊙ + \frac{μ_{0} i}{2 r} \otimes$

$B_{0} = \frac{μ_{0} i}{2 π r} (π - 1) \otimes$

$B \to B_{0} = \frac{μ_{0}}{4 π} \frac{i}{r} ⊙ + \frac{μ_{0}}{4 π} \frac{i}{r} π ⊙ + \frac{μ_{0}}{4 π} \frac{i}{r} π ⊙$

$= (\frac{2 μ_{0}}{4 π} \frac{i}{r} + \frac{μ_{0}}{4 π} \frac{i}{r} π) ⊙$

$B_{0} = \frac{μ_{0} i}{4 π r} (2 + π) ⊙$

$C \to B_{0} = \frac{μ_{0}}{4 π} \frac{i}{r} \otimes + \frac{μ_{0}}{4 π} \frac{i}{r} π \otimes + 0$

$B_{0} = \frac{μ_{0}}{4 π} \frac{i}{r} (1 + π) \otimes$

$D \to B_{0} = \frac{μ_{0}}{4 π} \frac{i}{r} π = \frac{μ_{0}}{4 π} \frac{i}{r} ⊙$

$A - III; B - I; C - IV; D - II$

Q 9 :

A single current carrying loop of wire carrying current $I$ flowing in anticlockwise direction seen from +ve $z$ direction and lying in $x y$ plane as shown in figure. The plot of $\hat{j}$ component of magnetic field $(B_{y})$ at a distance $' a'$ (less than radius of the coil) and on $y z$ plane vs $z$ coordinate looks like [2023]

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(3)

$B_{y} = 0 in the plane of the coil$

$B_{y} is opposite to each other at - z and + z positions.$

Q 10 :

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be [2023]

8 T
4 T
2 T
16 T

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(3)

$B = \frac{μ_{0} i}{2 R} \times 4 and B' = \frac{μ_{0} i}{2 R'}$

$For R' = 4 R \Rightarrow B' = \frac{μ_{0} i}{8 R}$

$\frac{B'}{B} = \frac{1}{16} \Rightarrow B' = 2 T$

Q 11 :

A long conducting wire having a current $I$ flowing through it is bent into a circular coil of $N$ turns. Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is [2023]

$N : n$
$n^{2} : N^{2}$
$N^{2} : n^{2}$
$n : N$

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(3)

$l = (2 π r) n$

$r \propto (\frac{l}{n})$

$B = n (\frac{μ_{0} i}{2 r}) \propto (\frac{μ_{0} i}{2 L}) n^{2}$

$\frac{B_{1}}{B_{2}} = (\frac{N^{2}}{n^{2}})$

Q 12 :

Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires. [2023]

$\frac{μ_{0} i}{2 r} (1 + \frac{2}{π})$
$\frac{μ_{0} i}{2 r} (1 + \frac{1}{π})$
$\frac{μ_{0} i}{2 r} (\frac{1}{2} + \frac{1}{2 π})$
$\frac{μ_{0} i}{2 r} (\frac{1}{2} + \frac{1}{π})$

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(3)

$B_{P} = (\frac{μ_{0} i}{4 r} + \frac{μ_{0} i}{4 π r}) = \frac{μ_{0} i}{2 r} (\frac{1}{2} + \frac{1}{2 π})$

Q 13 :

As shown in the figure, a long straight conductor with a semicircular arc of radius $\frac{π}{10} m$ is carrying current $I = 3 A$ . The magnitude of the magnetic field at the center $O$ of the arc is (The permeability of the vacuum $= 4 π \times 10^{- 7} {NA}^{- 2}$ ). [2023]

$6 μ T$
$1 μ T$
$4 μ T$
$3 μ T$

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(4)

$B_{C} = \frac{μ_{0} I}{4 π R} (π) (B at centre of circular arc)$

$= \frac{μ_{0} I}{4 R} = \frac{4 π \times 10^{- 7} \times 3}{4 \times \frac{π}{10}} = 3 \times 10^{- 6} T = 3 μ T$

Q 14 :

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of the coil on its axis is $\sqrt{x} : 1$ . The value of $x$ is _______. [2023]

(8)

$Magnetic field at centre (B_{1}) = \frac{μ_{0} I}{2 r}$

$Magnetic field on axis = \frac{μ_{0} I r^{2}}{2 {(r^{2} + d^{2})}^{3 / 2}}$

Value of $d = r$ (given)

$B_{2} = \frac{μ_{0} I}{4 \sqrt{2} r}$

$\frac{B_{1}}{B_{2}} = \frac{μ_{0} I}{2 r} \times \frac{4 \sqrt{2} r}{μ_{0} I} = \frac{2 \sqrt{2}}{1} = \frac{\sqrt{8}}{1}$

$\Rightarrow x = 8$

Q 15 :

Two identical circular wires of radius 20 cm and carrying current $\sqrt{2} A$ are placed in perpendicular planes as shown in the figure. The net magnetic field at the centre of the circular wires is ________ $\times 10^{- 8} T$ . [2023]

(Take $π = 3.14$ )

(628)

$Magnetic field B_{C} at center = \frac{μ_{0} i}{2 r}$

$B_{C} = \frac{4 π \times 10^{- 7}}{2 \times 0.2} \times \sqrt{2} T$

$Net magnetic field is$

$B_{C} \sqrt{2} = \frac{4 π \times 10^{- 7} \times \sqrt{2}}{2 \times 0.2} \times \sqrt{2} T = 2 π \times 10^{- 6} T$

$= 200 π \times 10^{- 8} T = 628 \times 10^{- 8} T$

Q 16 :

A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is _______ $\times 10^{- 4} T$ . [2023]

(2)

$B_{at O} = \frac{μ_{0} I}{4 R} = \frac{4 π \times 10^{- 7} \times 14}{4 \times 2.2 \times 10^{- 2}} = 2 \times 10^{- 4} T$

Q 17 :

Two identical circular loops P and Q each of radius $r$ are lying in parallel planes such that they have common axis. The current through P and Q are $I$ and $4 I$ respectively in clockwise direction as seen from O. The net magnetic field at O is: [2026]

$\frac{μ_{0} I}{4 \sqrt{2} r}$ towards Q
$\frac{3 μ_{0} I}{4 \sqrt{2} r}$ towards Q
$\frac{3 μ_{0} I}{4 \sqrt{2} r}$ towards P
$\frac{μ_{0} I}{4 \sqrt{2} r}$ towards P

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(2)

$B_{net} = B_{1} - B_{2}$

$= \frac{4 μ_{0} i R^{2}}{2 {(R^{2} + R^{2})}^{3 / 2}} - \frac{μ_{0} i R^{2}}{2 {(R^{2} + R^{2})}^{3 / 2}}$

$= \frac{3 μ_{0} i}{4 \sqrt{2} R}$

Q 18 :

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is : [2026]

$- \frac{μ_{0}}{2 π} \frac{I}{r} (π - 1) \hat{i}$
$\frac{μ_{0}}{2 π} \frac{I}{r} (π - 1) \hat{i}$
$- \frac{μ_{0}}{2 π} \frac{I}{r} (π + 1) \hat{i}$
$\frac{μ_{0}}{2 π} \frac{I}{r} (π + 1) \hat{i}$

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(1)

${\vec{B}}_{0} = {\vec{B}}_{A B} + {\vec{B}}_{D E} + {\vec{B}}_{B C D}$

$= \frac{μ_{0} i}{4 π r} \hat{i} + \frac{μ_{0} i}{4 π r} \hat{i} - \frac{μ_{0} i}{2 r} \hat{i}$

$= \frac{μ_{0} i}{2 π r} \hat{i} - \frac{μ_{0} i}{2 r} \hat{i}$

$= \frac{μ_{0} i}{2 π r} (1 - π) \hat{i}$

$= - \frac{μ_{0} i}{2 π r} (π - 1) \hat{i}$

Q 19 :

The magnetic field at the centre of a current carrying circular loop of radius R is $16 μ T$ . The magnetic field at a distance $x = \sqrt{3} R$ on its axis from the centre is______ $μ T$ . [2026]

2
$2 \sqrt{2}$
4
8

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(1)

$\frac{μ_{0} I}{2 R} = 16 μ T$

$\frac{μ_{0} I R^{2}}{2 {(x^{2} + R^{2})}^{3 / 2}} = \frac{μ_{0} I R^{2}}{2 \times 8 R^{3}} = 2 μ T$

Q 20 :

Three rings, each having equal radius R and carrying a current $I$ , are placed mutually perpendicular to each other such that each has its centre at the origin of coordinate system. The magnitude of the magnetic field at the common centre is $\sqrt{k} (\frac{μ_{0} I}{2 R})$ . Then the value of $k$ is

(3)

$\vec{B} = \frac{μ_{0} I}{2 R} (\pm \hat{i}) + \frac{μ_{0} I}{2 R} (\pm \hat{j}) + \frac{μ_{0} I}{2 R} (\pm \hat{k})$

$\Rightarrow$ $| \vec{B} |$ $= \frac{μ_{0} I}{2 R} \sqrt{3}$

Q 21 :

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $α \times 10^{- 14} J$ . The value of $α$ is ______. $(μ_{0} = 4 π \times 10^{- 7} Tm/A, π = 3.14)$ [2026]

$6.28$
$6.28 \times 10^{- 6}$
$628$
$6.28 \times 10^{- 4}$

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(1)

$Magnetic field at centre, B = \frac{μ_{0} N I}{2 R} = \frac{μ_{0} I}{2 R} (For N = 1)$

$So energy stored, U = \frac{B^{2}}{2 μ_{0}} \times V$

$U = \frac{1}{2 μ_{0}} \times \frac{μ_{0}^{2} I^{2}}{4 R^{2}} \times {(side)}^{3} = \frac{μ_{0} I^{2}}{8 R^{2}} \times {(10^{- 3})}^{3}$

$U = \frac{4 π \times 10^{- 7} \times 4}{8 \times 10^{- 2}} \times 10^{- 9} = 6.28 \times 10^{- 14} J$

Q 22 :

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are $B_{1}$ and $B_{2}$ respectively, then the ratio $\frac{B_{1}}{B_{2}}$ is ______. [2026]

$\frac{2 + π}{1 + π}$
$\frac{1 + π}{1 - π}$
$\frac{2 + π}{1 - π}$
$\frac{1 + π}{2 - π}$

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(1)

$B_{P} = \frac{μ_{0} i}{4 π r} \times 2 + \frac{μ_{0} i}{4 r} = \frac{μ_{0} i}{4 r} (1 + \frac{2}{π})$

$B_{Q} = \frac{μ_{0} i}{4 π r} + \frac{μ_{0} i}{4 r} = \frac{μ_{0} i}{4 r} (1 + \frac{1}{π})$

$\Rightarrow \frac{B_{P}}{B_{Q}} = \frac{1 + 2 / π}{1 + 1 / π} = \frac{π + 2}{π + 1}$

Topic Question Set

Q 1 :

Two insulated circular loops A and B of radius 'a' carrying a current of 'I' in the anti-clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be ______. [2024]

Q 2 :

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_{1} = 2 π m$ and $R_{2} = 4 π m$ , carrying current $I = 4 A$ as per figure given below is $α \times 10^{- 7} T$ . The value of $α$ is ______. (Centre O is common for all segments) [2024]

Q 4 :

An infinite wire has a circular bend of radius a, and carrying a current $I$ as shown in figure.

The magnitude of magnetic field at the origin O of the arc is given by: [2025]

Q 6 :

Let $B_{1}$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current $I$ . Let $B_{2}$ be the magnitude of magnetic field at an axial distance 'x' from the centre. For $x : R = 3 : 4, \frac{B_{2}}{B_{1}}$ is: [2025]

Q 8 :

Match the Column – I with Column – II: [2023]

Choose the correct answer from the options given below:

Q 10 :

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be [2023]

Q 12 :

Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires. [2023]

Q 13 :

As shown in the figure, a long straight conductor with a semicircular arc of radius $\frac{π}{10} m$ is carrying current $I = 3 A$ . The magnitude of the magnetic field at the center $O$ of the arc is (The permeability of the vacuum $= 4 π \times 10^{- 7} {NA}^{- 2}$ ). [2023]

Q 14 :

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of the coil on its axis is $\sqrt{x} : 1$ . The value of $x$ is _______. [2023]

Q 15 :

Two identical circular wires of radius 20 cm and carrying current $\sqrt{2} A$ are placed in perpendicular planes as shown in the figure. The net magnetic field at the centre of the circular wires is ________ $\times 10^{- 8} T$ . [2023]

(Take $π = 3.14$ )

Q 16 :

A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is _______ $\times 10^{- 4} T$ . [2023]

Q 17 :

Two identical circular loops P and Q each of radius $r$ are lying in parallel planes such that they have common axis. The current through P and Q are $I$ and $4 I$ respectively in clockwise direction as seen from O. The net magnetic field at O is: [2026]

Q 18 :

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is : [2026]

Q 19 :

The magnetic field at the centre of a current carrying circular loop of radius R is $16 μ T$ . The magnetic field at a distance $x = \sqrt{3} R$ on its axis from the centre is______ $μ T$ . [2026]

Q 21 :

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $α \times 10^{- 14} J$ . The value of $α$ is ______. $(μ_{0} = 4 π \times 10^{- 7} Tm/A, π = 3.14)$ [2026]

Q 22 :

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are $B_{1}$ and $B_{2}$ respectively, then the ratio $\frac{B_{1}}{B_{2}}$ is ______. [2026]

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Topic Question Set

Q 1 : Two insulated circular loops A and B of radius 'a' carrying a current of 'I' in the anti-clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be ______. [2024]

Q 2 : The magnetic field at the centre of a wire loop formed by two semicircular wires of radii R1=2πm and R2=4πm, carrying current I=4A as per figure given below is α×10-7T. The value of α is ______. (Centre O is common for all segments) [2024]

Q 4 : An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by: [2025]

Q 6 : Let B1 be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let B2 be the magnitude of magnetic field at an axial distance 'x' from the centre. For x : R=3 : 4, B2B1 is: [2025]

Q 7 : A loop ABCDA, carrying current I = 12A, is placed in a plane, consists of two semi-circular segments of radius R1=6 πm and R2=4 πm. The magnitude of the resultant magnetic field at center O is k×10–7 T. The value of k is _______ (Given μ0=4π×10–7 T mA–1) [2025]

Q 8 : Match the Column – I with Column – II: [2023] Choose the correct answer from the options given below:

Q 10 : The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be [2023]

Q 12 : Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires. [2023]

Q 13 : As shown in the figure, a long straight conductor with a semicircular arc of radius π10m is carrying current I=3 A. The magnitude of the magnetic field at the center O of the arc is (The permeability of the vacuum =4π×10-7 NA-2). [2023]

Q 14 : The ratio of magnetic field at the centre of a current carrying coil of radius r to the magnetic field at distance r from the centre of the coil on its axis is x:1. The value of x is _______. [2023]

Q 15 : Two identical circular wires of radius 20 cm and carrying current 2 A are placed in perpendicular planes as shown in the figure. The net magnetic field at the centre of the circular wires is ________ ×10-8 T. [2023] (Take π=3.14)

Q 16 : A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is _______ ×10-4 T. [2023]

Q 17 : Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O. The net magnetic field at O is: [2026]

Q 18 : An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is : [2026]

Q 19 : The magnetic field at the centre of a current carrying circular loop of radius R is 16μT. The magnetic field at a distance x=3R on its axis from the centre is______μT. [2026]

Q 20 : Three rings, each having equal radius R and carrying a current I, are placed mutually perpendicular to each other such that each has its centre at the origin of coordinate system. The magnitude of the magnetic field at the common centre is k(μ0I2R). Then the value of k is

Q 21 : A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is α×10-14 J. The value of α is ______. (μ0=4π×10-7 Tm/A, π=3.14) [2026]

Q 22 : Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are B1 and B2 respectively, then the ratio B1B2 is ______. [2026]

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Q 1 :

Two insulated circular loops A and B of radius 'a' carrying a current of 'I' in the anti-clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be ______. [2024]

Q 2 :

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_{1} = 2 π m$ and $R_{2} = 4 π m$ , carrying current $I = 4 A$ as per figure given below is $α \times 10^{- 7} T$ . The value of $α$ is ______. (Centre O is common for all segments) [2024]

Q 4 :

An infinite wire has a circular bend of radius a, and carrying a current $I$ as shown in figure.

The magnitude of magnetic field at the origin O of the arc is given by: [2025]

Q 6 :

Let $B_{1}$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current $I$ . Let $B_{2}$ be the magnitude of magnetic field at an axial distance 'x' from the centre. For $x : R = 3 : 4, \frac{B_{2}}{B_{1}}$ is: [2025]

Q 8 :

Match the Column – I with Column – II: [2023]

Choose the correct answer from the options given below:

Q 10 :

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn. The magnetic induction at the centre of the coil by the same current will be [2023]

Q 12 :

Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires. [2023]

Q 13 :

As shown in the figure, a long straight conductor with a semicircular arc of radius $\frac{π}{10} m$ is carrying current $I = 3 A$ . The magnitude of the magnetic field at the center $O$ of the arc is (The permeability of the vacuum $= 4 π \times 10^{- 7} {NA}^{- 2}$ ). [2023]

Q 14 :

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of the coil on its axis is $\sqrt{x} : 1$ . The value of $x$ is _______. [2023]

Q 15 :

Two identical circular wires of radius 20 cm and carrying current $\sqrt{2} A$ are placed in perpendicular planes as shown in the figure. The net magnetic field at the centre of the circular wires is ________ $\times 10^{- 8} T$ . [2023]

(Take $π = 3.14$ )

Q 16 :

A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is _______ $\times 10^{- 4} T$ . [2023]

Q 17 :

Two identical circular loops P and Q each of radius $r$ are lying in parallel planes such that they have common axis. The current through P and Q are $I$ and $4 I$ respectively in clockwise direction as seen from O. The net magnetic field at O is: [2026]

Q 18 :

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is : [2026]

Q 19 :

The magnetic field at the centre of a current carrying circular loop of radius R is $16 μ T$ . The magnetic field at a distance $x = \sqrt{3} R$ on its axis from the centre is______ $μ T$ . [2026]

Q 21 :

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $α \times 10^{- 14} J$ . The value of $α$ is ______. $(μ_{0} = 4 π \times 10^{- 7} Tm/A, π = 3.14)$ [2026]

Q 22 :

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are $B_{1}$ and $B_{2}$ respectively, then the ratio $\frac{B_{1}}{B_{2}}$ is ______. [2026]