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

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]

[IMAGE 235]

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

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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]

[IMAGE 236]

$6 μ T$
$1 μ T$
$4 μ T$
$3 μ T$

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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]

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(8)

[IMAGE 237]

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

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

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]

[IMAGE 238]

(Take $π = 3.14$ )

0%

(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]

[IMAGE 239]

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(2)

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

Topic Question Set

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]

[IMAGE 235]

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]

[IMAGE 236]

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]

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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]

[IMAGE 238]

(Take $π = 3.14$ )

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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]

[IMAGE 239]

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