Biot-Savart's Law and its application PYQs: JEE Mains Physics

Showing 1–50 of 50 questions

1. 1. 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 \(\alpha \times 10^{-14}\) J. The value of \(\alpha\) is _______. (\(\mu_o = 4\pi \times 10^{-7}\) Tm/A, \(\pi = 3.14\)) 2026 Hard
2. 2. 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 Medium
3. 3. The current passing through a conducting loop in the form of equilateral triangle of side \(4\sqrt{3}\) cm is 2A. The magnetic field at its centroid is \(\alpha\times10^{-5}T\). The value of \(\alpha\) is ___________.
   (Given : \(\mu_{o}=4\pi\times10^{-7}\) SI units) 2026 Medium
4. 4. The magnetic field at the centre of a current carrying circular loop of radius \(R\) is 16 \(\mu\)T. The magnetic field at a distance \(x = \sqrt{3}R\) on its axis from the centre is ________ \(\mu\)T. 2026 Medium
5. 5.
   
   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 Easy
6. 6. Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \(\dfrac{B_1}{B_2}\) is _______.
   2026 Hard
7. 7. A current of 5A exists in a square loop of side \(\frac{1}{\sqrt{2}} \mathrm{~m}\). Then the magnitude of the magnetic field \(B\) at the centre of the square loop will be \(p \times 10^{-6} \mathrm{~T}\). where, value of p is _____ .
   \(\left[\right.\) Take \(\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\). 2025 Medium
8. 8. A loop ABCDA , carrying current \(\mathrm{I}=12 \mathrm{~A}\), is placed in a plane, consists of two semi-circular segments of radius \(R_1=6 \pi \mathrm{~m}\) and \(\mathrm{R}_2=4 \pi \mathrm{~m}\). The magnitude of the resultant magnetic field at center O is \(\mathrm{k} \times 10^{-7} \mathrm{~T}\). The value of k is ______ (Given \(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\))
   2025 Medium
9. 9.
   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 Easy
10. 10. 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 Medium
11. 11. Figure shows a current carrying square loop ABCD of edge length is ' \(a\) ' lying in a plane. If the resistance of the \(A B C\) part is \(r\) and that of \(A D C\) part is 2 r , then the magnitude of the resultant magnetic field at centre of the square loop is
    2025 Hard
12. 12. 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 center. For \(x: R=3: 4, \frac{B_2}{B_1}\) is : 2025 Medium
13. 13. Two long parallel wires \(X\) and \(Y\), separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is \(x \times 10^{-5} \mathrm{~T}\). The value of \(x\) is__________ . Take permeability of free space as \(\mu_0=4 \pi \times 10^{-7} \mathrm{SI}\) units.
    2025 Easy
14. 14. A regular polygon of \(6\) sides is formed by bending a wire of length \(4 \pi\) meter. If an electric current of \(4 \pi \sqrt{3} \mathrm{~A}\) is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be \(x \times 10^{7} \mathrm{~T}\). The value of \(\mathrm{x}\) is ______. 2024 Hard
15. 15. An element \(\Delta l=\Delta \mathrm{xi}\) is placed at the origin and carries a large current \(\mathrm{I}=10 \mathrm{~A}\). The magnetic field on the \(y\)-axis at a distance of \(0.5 \mathrm{~m}\) from the elements \(\Delta \mathrm{x}\) of \(1 \mathrm{~cm}\) length is _______.
    2024 Hard
16. 16. The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______. 2024 Hard
17. 17. The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi\  \mathrm{m}\) and \(R_2=4 \pi\  \mathrm{m}\) carrying current \(I=4 \mathrm{~A}\) as per figure given below is \(\alpha \times 10^{-7} \mathrm{~T}\). The value of \(\alpha\) is___________ (Centre \(\mathrm{O}\) is common for all segments)
    2024 Hard
18. 18. Two circular coils \(P\) and \(Q\)of \(100\) turns each have same radius of \(\pi \mathrm{cm}\). The currents in \(\mathrm{P}\) and \(\mathrm{R}\) are \(1 \mathrm{~A}\) and \(2 \mathrm{~A}\) respectively. \(\mathrm{P}\) and \(\mathrm{Q}\) are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is \(\sqrt{\mathrm{x}} \mathrm{mT}\), where \(\mathrm{x}=\) _______. \(\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\) 2024 Hard
19. 19. Two insulated circular loop \(A\) and \(B\) radius ' \(a\) ' carrying a current of ' \(\mathrm{I}\) ' in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be _______.
    2024 Hard
20. 20. Two parallel long current carrying wire separated by a distance \(2 \mathrm{r}\) are shown in the figure. The ratio of magnetic field at \(\mathrm{A}\) to the magnetic field produced at \(C\) is \(\frac{x}{7}\). The value of \(x\) is _______.
    2024 Hard
21. 21. A circular loop of radius \(r\) is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance \(r\) from the center of the loop on its axis is: 2023 Medium
22. 22. A straight wire carrying a current of \(14\,A\) is bent into a semicircular are 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 Easy
23. 23. An electron in a hydrogen atom revolves around its nucleus with a speed of \(6.76 \times 10^6\,ms ^{-1}\) in an orbit of radius \(0.52\,\mathring A\). The magnetic field produced at the nucleus of the hydrogen atom is \(......T\). 2023 Medium
24. 24. As shown in the figure, a current of \(2\,A\) flowing in an equilateral triangle of side \(4 \sqrt{3}\,cm\). The magnetic field at the centroid \(O\) of the triangle is: (Neglect the effect of earth's magnetic field.)
    2023 Medium
25. 25. Find the magnetic field at the point \(P\) in figure. The curved portion is a semicircle connected to two long straight wires.
    2023 Medium
26. 26. Math List \(I\) with List \(II\) Choose the correct answer from the option given below:
    2023 Medium
27. 27. 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 \(..........\,T\) 2023 Easy
28. 28. The magnitude of magnetic induction at mid-point \(O\) due to current arrangement as shown in Fig will be
    2023 Medium
29. 29. Two identical circular wires of radius \(20\,cm\) and carrying current \(\sqrt{2}\,A\) are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wire is \(.............\times 10^{-8}\,T\). (Take \(\pi=3.14\) )
    2023 Medium
30. 30. A closely wounded circular coil of radius \(5\,cm\) produces a magnetic field of \(37.68 \times 10^{-4}\,T\) at its center. The current through the coil is \(......A\). [Given, number of turns in the coil is \(100\) and \(\pi=3.14]\) 2022 Easy
31. 31. \(B _{ X }\) and \(B _{ Y }\) are the magnetic field at the centre of two coils of two coils \(X\) and \(Y\) respectively, each carrying equal current. If coil \(X\) has \(200\) turns and \(20 cm\) radius and coil \(Y\) has \(400\) turns and \(20 cm\) radius, the ratio of \(B _{ X }\) and \(B _{ Y }\) is 2022 Medium
32. 32. The electric current in a circular coil of \(2\) turns produces a magnetic induction \(B _{1}\) at its centre. The coil is unwound and is rewound into a circular coil of \(5\) turns and the same current produces a magnetic induction \(B _{2}\) at its centre.The ratio of \(\frac{ B _{2}}{ B _{1}}\) is. 2022 Medium
33. 33. The magnetic field at the center of current carrying circular loop is \(B _{1}\). The magnetic field at a distance of \(\sqrt{3}\) times radius of the given circular loop from the center on its axis is \(B_{2}\). The value of \(B_{1} / B_{2}\) will be. 2022 Medium
34. 34. The magnetic field at the centre of a circular coil of radius \(I\), due to current I flowing through it, is \(B\). The magnetic field at a point along the axis at a distance \(\frac{r}{2}\) from the centre is 2022 Medium
35. 35. A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point \(P\) which lies on the centre of the semicircle ?
    2021 Hard
36. 36. Magnetic fields at two points on the axis of a circular coil at a distance of \(0.05\, m\) and \(0.2\, m\) from the centre are in the ratio \(8: 1.\) The radius of coil is .......... \(m\) 2021 Hard
37. 37. The fractional change in the magnetic field intensity at a distance \('r'\) from centre on the axis of current carrying coil of radius \('a'\) to the magnetic field intensity at the centre of the same coil is : (Take \(r << a )\) 2021 Hard
38. 38. There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is \(1: 1\). The magnetic field at point \(P\) is ...... .
    2021 Hard
39. 39. A very long wire \(ABDMNDC\) is shown in figure carrying current \(I. AB\) and \(BC\) parts are straight, long and at right angle. At \(D\) wire forms a circular turn \(DMND\) of radius \(R. AB.\) \(\mathrm{BC}\) parts are tangential to circular turn at \(\mathrm{N}\) and \(D\). Magnetic field at the centre of circle is
    2020 Hard
40. 40. A wire \(A\), bent in the shape of an arc of a circle, carrying a current of \(2\, A\) and having radius \(2\, cm\) and another wire \(B ,\) also bent in the shape of arc of a circle, carrying a current of \(3\, A\) and having radius of \(4\, cm ,\) are placed as shown in the figure. The ratio of the magnetic fields due to the wires \(A\) and \(B\) at the common centre \(O\) is
    2020 Hard
41. 41. Magnitude of magnetic field (in \(SI\) units) at the centre of a hexagonal shape coil of side \(10\, cm\), \(50\) turns and carrying current \(I\) (Ampere) in units of \(\frac{\mu_{0} I}{\pi}\) is 2020 Hard
42. 42. A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of \(10\, A\). The magnetic field at point \(O\) will be close to
    2019 Medium
43. 43. A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi  \times {{10}^{ - 7}}\,N/{A^2}} \right)\) 2019 Medium
44. 44. As shown in the figure, two infinitely long, identical wires are bent by \(90^o\) and placed in such a way that the segments \(LP\) and \(QM\) are along the \(x-\) axis, while segments \(PS\) and \(QN\) are parallel to the \(y-\) axis. If \(OP = OQ = 4\, cm\), and the magnitude of the magnetic field at \(O\) is \(10^{-4}\, T\), and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at \(O\) will be \((\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})\)
    2019 Hard
45. 45. Find the magnetic field at point \(P\) due to a straight line segment \(AB\) of length \(6\, cm\) carrying a current of \(5\, A\). (See figure) \((\mu _0 = 4p\times10^{-7}\, N-A^{-2})\)
    2019 Hard
46. 46. One of the two identical conducing wires of length \(L\) is bent in the form of a circular loop and the other one into a circular coil of \(N\) identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \((B_L)\) to that at the centre of the coil \((B_C),\); \(.\,\frac {B_L}{B_C}\) will be 2019 Medium
47. 47. Two very long, straight and insulated wires are kept at \(90^o\) angle from each other In \(xy -\) plane as shown in the figure. These wires carry current of equal magnitude \(I\), whose directions are shown in the figure. The net magnetic field at point \(P\) will be
    2019 Medium
48. 48. A Helmholtz coil has pair of loops, each with \(N\) turns and radius \(R\). They are placed coaxially at distance \(R\) and the same current \(I\) flows through the loops in the same direction. The magnitude of magnetic field at \(P\), midway between the centres \(A\) and \(C\), is given by (Refer to figure)
    2018 Hard
49. 49. Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field \(B_1,\) at its centre when a current \(I\) passes through it.The second wire is bent into a coil with  three identical loops adjacent to each other and produces magnetic field \(B_2\) at the centre of the loops when current \(I/3\) passes through it. The ratio \(B_1 : B_2\) is 2014 Hard
50. 50. A parallel plate capacitor of area \(60\, cm^2\) and separation \(3\, mm\) is charged initially to \(90\, \mu C\). If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of \(2.5\times10^{-8}\, C/s\), then what is the magnetic field between the plates ? 2013 Medium

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