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)

$\frac{μ_{0} I}{2 R} = 16 μ T$

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

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]

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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]

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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]