Magnetic Moment of Current Carrying Coil and Torque and Work Done in Rotating the Coil PYQs: JEE Mains Physics

Showing 1–29 of 29 questions

1. 1. A circular coil of radius \(2\) cm and \(125\) turns carries a current of \(1\) A. The coil is placed in a uniform magnetic field of magnitude \(0.4\) T. The axis of the coil makes an angle of \(30°\) with the direction of the magnetic field. The torque acting on the coil is \(\alpha \times 10^{-4}\) N.m. The value of \(\alpha\) is ______.
   (\(\pi=3.14\)) 2026 Medium
2. 2. A current carrying circular loop of radius \(2\) cm with unit normal \(\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field, \(\vec{B} = B_0(3\hat{i}+2\hat{k})\). If \(B_0 = 4\times 10^{-3}\) T and current \(I=100\sqrt{2}\) A, the torque experienced by the loop is ________ Wb·A. (\(\pi=3.14\)) 2026 Hard
3. 3. A particle of charge \(q\) and mass \(m\) is projected from origin with an initial velocity \(\vec{v} = \left(\dfrac{v_0}{\sqrt{2}}\hat{x} + \dfrac{v_0}{\sqrt{2}}\hat{y}\right)\). There exists a uniform magnetic field \(\vec{B} = B_0 \hat{z}\) and a space varying electric field \(\vec{E} = E_0 e^{-\lambda x}\hat{x}\) within the region \(0 \leq x \leq L\). After travelling a distance such that \(x\)-coordinate has changed from \(x=0\) to \(x=L\), the change in the kinetic energy is _______. 2026 Hard
4. 4. An insulated wire is wound so that it forms a flat coil with \(N = 200\) turns. The radius of the innermost turn is \(r_1 = 3\) cm, and of the outermost turn \(r_2 = 6\) cm. If \(20\) mA current flows in it then the magnetic moment will be \(\alpha \times 10^{-2}\) A.m\(^2\). The value of \(\alpha\) is _____. 2026 Medium
5. 5. A circular coil having \(200\) turns, \(2.5 \times 10^{-4} \mathrm{~m}^2\) area and carrying \(100 \mu \mathrm{A}\) current is placed in a uniform magnetic field of \(1 \mathrm{~T}\). Initially the magnetic dipole moment \((\vec{M})\) was directed along \(\vec{B}\). Amount of work, required to rotate the coil through \(90^{\circ}\) from its initial orientation such that \(\overrightarrow{\mathrm{M}}\) becomes perpendicular to \(\vec{B}\) is _______ \(\mu \mathrm{J}\). 2024 Hard
6. 6. A coil having \(100\) turns, area of \(5 \times 10^{-3} \mathrm{~m}^2\), carrying current of \(1 \mathrm{~mA}\) is placed in uniform magnetic field of \(0.20 \mathrm{~T}\) such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through \(90^{\circ}\) is _______ \(\mu \mathrm{J}\). 2024 Hard
7. 7. A uniform magnetic field of \(2 \times 10^{-3} \mathrm{~T}\) acts along positive \(\mathrm{Y}\)-direction. A rectangular loop of sides \(20\) \(\mathrm{cm}\) and \(10 \mathrm{~cm}\) with current of \(5 \mathrm{~A}\) is \(\mathrm{Y}-\mathrm{Z}\) plane. The current is in anticlockwise sense with reference to negative \(\mathrm{X}\) axis. Magnitude and direction of the torque is _______. 2024 Hard
8. 8. The magnetic moment of a bar magnet is \(0.5 \mathrm{Am}^2\). It is suspended in a uniform magnetic field of \(8 \times 10^{-2} \mathrm{~T}\). The work done in rotating it from its most stable to most unstable position is _______. 2024 Hard
9. 9. A massless square loop, of wire of resistance \(10\,\Omega\). supporting a mass of \(1\,g\). hangs vertically with one of its sides in a uniform magnetic field of \(10^3\, G\), directed outwards in the shaded region. A dc voltage \(V\) is applied to the loop. For what value of V. the magnetic force will exactly balance the weight of the supporting mass of \(1\,g\) ? (If sides of the loop \(=10\,cm , g =10\,ms ^{-2}\) )
   2023 Medium
10. 10. A wire of length \(314\,cm\) carrying current of \(14\,A\) is bent to form a circle. The magnetic moment of the coil is \(........A- m ^{2}\). [Given \(\left.\pi=3.14\right]\)
    2022 Medium
11. 11. The magnetic moment of an electron \((e)\) revolving in an orbit around nucleus with an orbital angular momentum is given by : 2022 Medium
12. 12. Two concentric circular loops of radii \(r _{1}=30\,cm\) and \(r_{2}=50\,cm\) are placed in \(X - Y\) plane as shown in the figure. \(A\) current \(I=7\,A\) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately.
    2022 Medium
13. 13. A charge \(Q\) is moving \(\overrightarrow{dl}\) distance in the magnetic field \(\overrightarrow{ B }\). Find the value of work done by \(\overrightarrow{ B }\). 2021 Medium
14. 14. A coil in the shape of an equilateral triangle of side \(10\, {cm}\) lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field \(20\, {mT}\). The torque acting on the coil when a current of \(0.2\, {A}\) is passed through it and its plane becomes parallel to the magnetic field will be \(\sqrt{{x}} \times 10^{-5} \,{Nm}\). The value of \({x}\) is ..... . 2021 Medium
15. 15. A uniform conducting wire of length is \(24 {a}\), and resistance \({R}\) is wound up as a current carrying coil in the shape of an equilateral triangle of side \('a'\) and then in the form of a square of side \('a'.\) The coil is connected to a voltage source \({V}_{0}\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is \(1: \sqrt{y}\) where \(y\) is ..... . 2021 Hard
16. 16. A charged particle going around in a circle can be considered to be a current loop. A particle of mass \(m\) carrying charge \(q\) is moving in a plane with speed \(v\) under the influence of magnetic field \(\overrightarrow{ B }\). The magnetic moment of this moving particle 2020 Hard
17. 17. A circular coil has moment of inertia \(0.8 \,kg m ^{2}\) around any diameter and is carrying current to roduce a magnetic moment of \(20\, Am ^{2}\). The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of \(4\, T\) is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by \(60^{\circ}\) will be 2020 Hard
18. 18. A galvanometer coil has \(500\) turns and each turn has an average area of \(3 \times 10^{-4}\, m ^{2}\). If a torque of \(1.5\,Nm\) is required to keep this coil parallel to magnetic field when a current of \(0.5\, A\) is flowing through it, the strength of the field (in \(T )\) is 2020 Medium
19. 19. A small circular loop of conducting wire has radius \(a\) and carries current \(I\). It is placed in a uniform magnetic field \(\mathrm{B}\) perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period \(T\). If the mass of the loop is \(m\) then  2020 Medium
20. 20. A square loop of side \(2\, a ,\) and carrying current I, is kept in \(XZ\) plane with its centre at origin. A long wire carrying the same current \(I\) is placed parallel to the \(z-\)axis and passing through the point \((0, b, 0),(b>>a)\). The magnitude of the torque on the loop about \(z-\)axis is given by: 2020 Hard
21. 21. A square loop of side \(2a\) and carrying current I is kept in \(xz\) plane with its centre at origin. A long wire carrying the same current I is placed parallel to \(z-\)axis and passing through point \((0, b , 0),( b >> a ) .\) The magnitude of torque on the loop about \(z-\)ax is will be 2020 Hard
22. 22. A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is
    2020 Hard
23. 23. A circular coil having \(N\,turns\) and radius \(r\) carries a current. It is held in the \(XZ\) plane in a magnetic field \(B\hat i\) . The torque on the coil due to the magnetic field is 2019 Hard
24. 24. A rectangular coil (Dimension \(5\,cm\times 2\,cm\) ) with \(100\,turns,\) carrying a current of \(3\,A\) in the clock-wise direction, is kept centered at the origin and in the \(X-Z\) plane. A magnetic field of \(1\,T\) is applied along \(X-\) axis. If the coil is tilted through \(45^o\) about \(Z-\) axis, then the torque on the coil is.....\(Nm\) 2019 Medium
25. 25. A square loop is carrying a steady current \(I\) and the magnitude of its magnetic dipole moment is \(m\). If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be 2019 Medium
26. 26. An insulating thin rod of length \(l\) has a linear charge density \(\rho \left( x \right) = {\rho _0}\,\frac{x}{l}\) on it. The rod is rotated about an axis passing through the origin \((x = 0)\) and perpendicular to the rod. If the rod makes \(n\) rotations per second, then the time averaged magnetic moment of the rod is 2019 Hard
27. 27. A charge \(q\)  is spread uniformly over an insulated loop of radius \(r\) . If it is rotated with an angular velocity \(\omega \) with respect to normal axis then the magnetic moment of the loop is 2018 Medium
28. 28. The dipole moment of a circular loop carrying a current \(I\), is \(m\) and the magnetic field at the centre of the loop is \(B_1\) . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is \(B_2\) . The ratio \(\frac{{{B_1}}}{{{B_2}}}\) is 2018 Medium
29. 29. A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)
    2014 Hard

No questions on this page match these filters. Clear filters