Ampere's circuital law and its application (Solenoid and Toroid) PYQs: JEE Mains Physics

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1. 1. A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :
   A. maximum at either ends of the conductor and minimum at the midpoint
   B. maximum at the axis of the conductor
   C. minimum at the surface of the conductor
   D. minimum at the axis of the conductor
   E. same at all points in the cross-section of the conductor
   Choose the correct answer from the options given below : 2026 Hard
2. 2.
   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 \(\omega\) 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 Medium
3. 3. The magnetic field inside a 200 turns solenoid of radius 10 cm is \(2.9 \times 10^{-4} \mathrm{Tesla}\). If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ \(\pi \mathrm{cm}\). 2025 Easy
4. 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 Hard
5. 5. A solenoid of length \(0.5 \mathrm{~m}\) has a radius of \(1 \mathrm{~cm}\) and is made up of ' \(m\) ' number of turns. It carries a current of \(5 \mathrm{~A}\). If the magnitude of the magnetic field inside the solenoid is \(6.28 \times 10^{-3} \mathrm{~T}\), then the value of \(m\) is _______. 2024 Hard
6. 6. 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 Hard
7. 7. Match List-\(I\) with List-\(II\) Choose the correct answer from the options given below :
   2024 Hard
8. 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 \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\) 2023 Easy
9. 9. 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 Medium
10. 10. Two long parallel wires carrying currents \(8\,A\) and \(15\,A\) in opposite directions are placed at a distance of \(7\,cm\) from each other. A point \(P\) is at equidistant from both the wires such that the lines joining the point \(P\) to the wires are perpendicular to each other. The magnitude of magnetic field at \(P\) is \(............\times 10^{-6}\,T\). (Given : \(\left.\sqrt{2}=1.4\right)\) 2023 Hard
11. 11. A long straight wire with a circular crosssection having radius \(R\), is carrying a steady current \(I\). The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance \(r\;( r < R )\) from its centre will be 2022 Easy
12. 12. The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to \(1.2 \times 10^{-5}\). What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid? 2022 Medium
13. 13. A coaxial 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 is, 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 \((ii)\) \({a}<{x}<{b}\) ? 2021 Hard
14. 14. 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 \(\left.=4 \pi \times 10^{-7} H / m \right)\) 2021 Medium
15. 15. 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 2020 Hard
16. 16. The magnitude of the magnetic field at the centre of an equilateral triangular loop of side \(1\,m\) which is carrying a current of \(10\,A\) is:......\(\mu T\) [Take \(\mu _0 = 4\pi  \times 10^{-7}\,NA^{-2}\)] 2019 Medium
17. 17. A current of \(1\,A\) is flowing on the sides of an equilateral triangle of side \(4.5\times10^{-2}\,m\) . The magnetic field at the centre of the triangle will be 2018 Hard
18. 18. A current \(i\) is flowing in a straight conductor of length \(L.\) The magnetic induction at a point on its axis at a distance \(\frac {L}{4}\) from its centre will be 2013 Medium

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