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

Q 1 :

Given below are two statements:

Statement (I): When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account.

Statement (II): Ampere's circuital law does not depend on Biot-Savart's law.

In the light of the above statements, choose the correct answer from the options given below: [2024]

Both Statement I and Statement II are false.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.

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(2)

Statement $I^{s t}$ is true

Statement $I I^{n d}$ is false as Ampere's law depends on Biot Savart's law.

Q 2 :

A solenoid of length 0.5 m has a radius of 1 cm and is made up of $' m'$ number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{- 3} T$ then the value of $m$ is _______ . [2024]

0%

(500) $μ_{0} n i = B$

$n$ = number of turns per unit length

$μ_{0} (\frac{m}{l}) i = B$

$m = \frac{B . l}{μ_{0} i} = \frac{6.28 \times 10^{- 3} \times 0.5}{12.56 \times 10^{- 7} \times 5} = 500$

Q 3 :

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero [2024]

outside the cable
in between the two conductors
inside the inner conductor
inside the outer conductor

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(1)

$\oint \vec{B} \cdot d \vec{ℓ} = μ_{0} i_{enc} = 0 ∴ B = 0 outside the cable$

Q 4 :

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 $2 a$ from axis of the wire is ______. [2024]

1 : 1
3 : 4
1 : 4
4 : 1

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(1)

Magnetic field inside wire,

$B_{inside} = \frac{μ_{0} J r}{2} = \frac{μ_{0} I r}{2 A} = \frac{μ_{0} I r}{2 π a^{2}}$

$r \to \frac{a}{2} \Rightarrow B_{inside} = \frac{μ_{0} I}{4 π a}$

Magnetic field outside, $B_{2} = \frac{μ_{0} i}{2 π r}$

$B_{2} = \frac{μ_{0} i}{2 π (2 a)} = \frac{μ_{0} i}{4 π a}$

$B_{inside} = \frac{μ_{0} I}{4 π a}$

So $B_{1} = B_{2} \Rightarrow 1 : 1$

Q 5 :

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 [2025]

[Ampere's Law]

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(1)

We know inside the wire

$B = \frac{μ_{0} I}{2 π a^{2}} \cdot r$ (0 < r < a)

And $B = \frac{μ_{0} I}{2 π r}$ for (r > a)

Option (1) is correct answer.

Q 6 :

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 $ω$ 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 [2025]

$\frac{N^{2}}{2 π} q ω$
$\frac{2 π}{N} q ω$
$\frac{N}{2 π} q ω$
$\frac{N}{π} q ω$

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(3)

$I = \frac{N q}{\frac{2 π}{ω}} = \frac{N q ω}{2 π}$

Now for bigger Amperian loop (loop B)

$I_{B (enclosed)} = 0$

And for smaller Amperian loop (loop A)

$| I_{A (enclosed)} | = I = \frac{N q ω}{2 π}$

So, $| I_{A} - I_{B} | = \frac{N q ω}{2 π}$

Q 7 :

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{- 4} Tesla$ . If the solenoid carries a current of 0.29A, then the length of the solenoid is ______ $π$ cm. [2025]

0%

(8)

Assuming long solenoid, magnetic field inside a solenoid

$B = μ_{0} i (\frac{N}{L})$

$L = \frac{μ_{0} N i}{B} = \frac{4 π \times 10^{- 7} \times 200 \times 0.29}{2.9 \times 10^{- 4}} = 8 π cm$

Q 8 :

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 __________. $(μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1})$ [2023]

$88 \times 10^{- 4} T$
$1232 \times 10^{- 4} T$
$352 \times 10^{- 4} T$
$176 \times 10^{- 4} T$

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(4)

$B = μ_{0} n I = 4 π \times 10^{- 7} \times 70 \times 10^{2} \times 2$

$= 56 π \times 10^{- 4} T = 176 \times 10^{- 4} T$

Q 9 :

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is [2023]

$2.4 \times 10^{3} {Am}^{- 1}$
$1.2 \times 10^{3} {Am}^{- 1}$
$1 {Am}^{- 1}$
$2.4 \times 10^{- 3} {Am}^{- 1}$

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(2)

$B = μ_{0} n i = μ_{0} \frac{N}{l} i$

$= 4 π \times 10^{- 7} \times \frac{1200}{2} \times 2 = 48 π \times 10^{- 5} T$

$H = \frac{B}{μ_{0}} = \frac{48 π \times 10^{- 5}}{4 π \times 10^{- 7}} = 12 \times 10^{2} = 1.2 \times 10^{3} A/m$

Q 10 :

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 [2023]

directly proportional to $r$ in the region $r < a$ and inversely proportional to $r$ in the region $r > a$
zero in the region $r < a$ and inversely proportional to $r$ in the region $r > a$
uniform in the region $r < a$ and inversely proportional to distance $r$ from the axis in the region $r > a$
inversely proportional to $r$ in the region $r < a$ and uniform throughout in the region $r > a$

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(1)

$B = {\begin{matrix} \frac{μ_{0} I r}{π a^{2}} & r \leq a \\ \frac{μ_{0} I}{π a^{2}} & r \geq a \end{matrix}$

Topic Question Set

Q 2 :

A solenoid of length 0.5 m has a radius of 1 cm and is made up of $' m'$ number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{- 3} T$ then the value of $m$ is _______ . [2024]

0%

Q 3 :

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero [2024]

Q 4 :

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 $2 a$ from axis of the wire is ______. [2024]

Q 5 :

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 [2025]

Q 7 :

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{- 4} Tesla$ . If the solenoid carries a current of 0.29A, then the length of the solenoid is ______ $π$ cm. [2025]

0%

Q 8 :

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 __________. $(μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1})$ [2023]

Q 9 :

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is [2023]

Q 10 :

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 [2023]

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