STD 12 - Electric charges and fields PYQs: JEE Mains Physics

Showing 1–50 of 161 questions

1. 1. A point charge \(q = 1\ \mu\text{C}\) is located at a distance \(2\text{ cm}\) from one end of a thin insulating wire of length \(10\text{ cm}\) having a charge \(Q = 24\ \mu\text{C}\), distributed uniformly along its length, as shown in figure. Force between \(q\) and wire is _______ N.
   (Use \(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2\))
   2026 Easy
2. 2. A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\vec{E}_1=E_0\hat{x}\). If another electric field \(\vec{E}_2=2E_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)? 2026 Hard
3. 3. A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the final tension in the string changes.The final tension in the string, when pendulum attains an equilibrium position is __________ .
   (g: acceleration due to gravity) 2026 Hard
4. 4. A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\)) 2026 Medium
5. 5. Identify the correct statements :
   A. Electrostatic field lines form closed loops.
   B. The electric field lines point radially outward when charge is greater than zero.
   C. The Gauss-Law is valid only for inverse-square force.
   D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
   E. The motion of a particle under Coulomb's force must take place in a plane.
   Choose the correct answer from the options given below : 2026 Medium
6. 6. Six point charges are kept \( 60^{\circ} \) apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is __________ .
   (\( \epsilon \) is permittivity of free space)
   2026 Hard
7. 7. Three charges +2q. +3q and -4q are situated at (0,-3a), (2a, 0) and (-2a,0) respectively in the xy plane. The resultant dipole moment about origin is _________ 2026 Easy
8. 8. Two point charges \(2 q\) and \(q\) are placed at vertex \(A\) and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :
   2026 Easy
9. 9. Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______. 2026 Medium
10. 10. Two point charges \(q_1=3\,\mu C\) and \(q_2=-4\,\mu C\) are placed at points \((2\hat{i}+3\hat{j}+3\hat{k})\) and \((\hat{i}+\hat{j}+\hat{k})\) respectively. Force on charge \(q_2\) is ________ N. \(\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^9 \text{ SI Units}\right)\) 2026 Medium
11. 11. Two short electric dipoles \(A\) and \(B\) having dipole moment \(p_1\) and \(p_2\) respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point \(x\) is making an angle of \(60°\) with the line joining points \(O\) and \(x\). The ratio of the dipole moments \(p_2/p_1\) is _______.
    2026 Hard
12. 12. Two shorts dipoles \((A, B), A\) having charges \(\pm 2 \mu C\) and length 1 cm and \(B\) having charges \(\pm 4 \mu C\) and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point \(P\), equi-distant from the centres of both dipoles is ___________ N/C.
    2026 Easy
13. 13. A dipole with two electric charges of \(2 \mu \mathrm{C}\) magnitude each, with separation distance \(0.5 \mu \mathrm{~m}\), is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by \(30^{\circ}\) from the axis, it tends to realign in the direction due to a torque. The value of torque is : 2025 Medium
14. 14. A line charge of length \(\frac{\text { ' } a \text { ' }}{2}\) is kept at the center of an edge \(B C\) of a cube \(A B C D E F G H\) having edge length ' \(a\) ' as shown in the figure. If the density of line charge is \(\lambda\) C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, \(\epsilon_0\) as the free space permittivity)
    
    
    2025 Hard
15. 15. A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?
    2025 Hard
16. 16. A particle of mass ' \(m\) ' and charge ' \(q\) ' is fastened to one end ' \(A\) ' of a massless string having equilibrium length \(l\), whose other end is fixed at point ' \(O\) '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is
    2025 Hard
17. 17. A point charge causes an electric flux of \(-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}\) to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
    (Given \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) ) 2025 Easy
18. 18. A point charge +q is placed at the origin. A second point charge +9 q is placed at \((\mathrm{d}, 0,0)\) in Cartesian coordinate system. The point in between them where the electric field vanishes is : 2025 Easy
19. 19. A point particle of charge \(Q\) is located at \(P\) along the axis of an electric dipole 1 at a distance \(r\) as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance \(2 a\). For the charge particle at P not to experience any net force, which of the following correctly describes the situation?
    
    2025 Hard
20. 20. A positive ion \(A\) and a negative ion \(B\) has charges \(6.67 \times 10^{-19} \mathrm{C}\) and \(9.6 \times 10^{-10} \mathrm{C}\), and masses \(19.2 \times 10^{-27} \mathrm{~kg}\) and \(9 \times 10^{-27} \mathrm{~kg}\) respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is \(P \times 10^{45}\), where the value of 10\(P\) is _______.
    (Take \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}\) and universal gravitational constant as \(6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\) )
    Assume that charge may not be an integral multiple of electrons. 2025 Medium
21. 21. A small bob of mass 100 mg and charge \(+10 \mu \mathrm{C}\) is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' \(\sigma\) ' as shown in figure. If string subtends an angle of \(45^{\circ}\) with the sheet at equilibrium the charge density of sheet will be :
    (Given, \(\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}\) and acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\))
    2025 Medium
22. 22. A small uncharged conducting sphere is placed in contact with an identical sphere but having \(4 \times 10^{-8} \mathrm{C}\) charge and then removed to a distance such that the force of repulsion between them is \(9 \times 10^{-3} \mathrm{~N}\). The distance between them is (Take \(\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\) as \(9 \times 10^9 \mathrm{in} \mathrm{SI}\) units) 2025 Hard
23. 23. A square loop of sides \(a=1 \mathrm{~m}\) is held normally in front of a point charge \(\mathrm{q}=1 \mathrm{C}\). The flux of the electric field through the shaded region is \(\frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}\), where the value of p is _____.
    
    2025 Easy
24. 24. An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \(\sigma_{\mathrm{o}}\). Choose the correct option from the following.
    
    2025 Medium
25. 25. An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J. 2025 Medium
26. 26. An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be: 2025 Medium
27. 27. An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \(10^6 \mathrm{~m} / \mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1 \mathrm{~V} / \mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) ) 2025 Medium
28. 28. An infinitely long wire has uniform linear charge density \(\lambda=2 \mathrm{nC} / \mathrm{m}\). The net flux through a Gaussian cube of side length \(\sqrt{3} \mathrm{~cm}\), if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \(\mathrm{xNm}^2 \mathrm{C}^{-1}\), where x is :
    [Neglect any edge effects and use \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) SI units] 2025 Easy
29. 29. Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin : 2025 Easy
30. 30. Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \(+\sigma\) and \(-2 \sigma\). The force experienced by a point charge +q placed at the mid point between two plates will be :
    2025 Hard
31. 31. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.
    Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
    In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Easy
32. 32. Match List - I with List - II.

    List - I	List - II
    (A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
    (B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
    (C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
    (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)

    Choose the correct answer from the options given\(\text{ }\)below\(\text{ }\): 2025 Medium
33. 33. The electric field in a region is given by \(\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^3 \mathrm{~N} / \mathrm{C}\). The flux of the field through a rectangular surface parallel to \(x-z\) plane is \(6.0 \mathrm{Nm}^2 \mathrm{C}^{-1}\). The area of the surface is ________ \(\mathrm{cm}^2\). 2025 Easy
34. 34. Two infinite identical charged sheets and a charged spherical body of charge density ' \(\rho\) ' are arranged as shown in figure. Then the correct relation between the electrical fields at \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D points is :
    2025 Medium
35. 35. Two small spherical balls of mass 10 g each with charges \(-2 \mu \mathrm{C}\) and \(2 \mu \mathrm{C}\), are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of \(100 \mu \mathrm{C} / \mathrm{m}^2\) such that length of rod makes an angle of \(30^{\circ}\) with electric field generated by charge sheet. Net torque acting on the rod is:
    (Take \(\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\)) 2025 Easy
36. 36. A charge \(q\) is placed at the center of one of the surface of a cube. The flux linked with the cube is _______. 2024 Hard
37. 37. A particle of charge \(-q\) and mass \(m\) moves in a circle of radius \(r\) around an infinitely long line charge of linear density \(+\lambda\). Then time period will be given as _______. (Consider \(k\) as Coulomb's constant) 2024 Hard
38. 38. A thin metallic wire having cross sectional area of \(10^{-4} \mathrm{~m}^2\) is used to make a ring of radius \(30 \mathrm{~cm}\). A positive charge of \(2 \pi \mathrm{C}\) is uniformly distributed over the ring, while another positive charge of \(30\) \(\mathrm{pC}\) is kept at the centre of the ring. The tension in the ring is__________ \(\mathrm{N}\); provided that the ring does not get deformed (neglect the influence of gravity). (given, \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\) units) 2024 Hard
39. 39. An electric field, \(\overrightarrow{\mathrm{E}}=\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^2\) area having unit vector \(\hat{\mathrm{n}}=\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)\). The electric flux for that surface is _______ \(\mathrm{Vm}\) 2024 Hard
40. 40. An electric field \(\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}\) exists in space. \(\mathrm{A}\) cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is _______ \(\mathrm{Nm}^2 / \mathrm{C}\)
    2024 Hard
41. 41. An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______. 2024 Hard
42. 42. An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(S\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of 1 m from \(S\) and has a speed of \(1 m s ^{-1}\). The maximum value of \(\sigma\), if the electron strikes \(S\) at \(t=1 s\) is \(\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{ C }{ m ^2}\). The value of \(\alpha\) is __________ . 2024 Medium
43. 43. An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______. 2024 Hard
44. 44. \(C_1\) and \(C_2\) are two hollow concentric cubes enclosing charges \(2 Q\) and \(3 Q\) respectively as shown in figure. The ratio of electric flux passing through \(C_1\) and \(C_2\) is _______.
    2024 Medium
45. 45. Five charges \(+q,+5 q,-2 q,+3 q\) and \(-4 q\) are situated as shown in the figure. The electric flux due to this configuration through the surface \(S\) is _______.
    2024 Hard
46. 46. Force between two point charges \(q_1\) and \(q_2\) placed in vacuum at ' \(r\) ' \(\mathrm{cm}\) apart is \(F\). Force between them when placed in a medium having dielectric \(\mathrm{K}=5\) at ' \(\mathrm{r} / 5\) ' \(\mathrm{cm}\) apart will be _______. 2024 Hard
47. 47. If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(\mathrm{x}=\) _______.
    2024 Hard
48. 48. In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of _______. 2024 Hard
49. 49. \(\sigma\) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is _______. 2024 Hard
50. 50. Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \mathrm{~N} / \mathrm{C}\) normally. A charged particle of mass \(2 \mathrm{~g}\) being suspended through a silk thread of length \(20 \mathrm{~cm}\) and remain stayed at a distance of \(10 \mathrm{~cm}\) from the wall. Then the charge on the particle will be \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)] 2024 Hard

No questions on this page match these filters. Clear filters