STD 12 - Electric charges and fields PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 161 questions

51. 51. The electric potential at the surface of an atomic nucleus \((Z=50)\) of radius \(9 \times 10^{-13} cm\) is \(\alpha \times 10^6 V\). What is the value of \(\alpha\)?
    (Charge of proton \(1.6 \times 10^{-19} C\) ) 2024 Medium
52. 52. Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point \(P\) is \(\frac{x \sigma}{\epsilon_0}\). The value of \(x\) is _______. (all quantities are measured in \(SI\) units).
    2024 Hard
53. 53. Two charges of \(-4 \ \mu \mathrm{C}\) and \(+4\  \mu \mathrm{C}\) are placed at the points \(A(1,0,4) \mathrm{m}\) and \(B(2,-1,5) \mathrm{m}\) located in an electric field \(\vec{E}=0.20 \hat{\mathrm{i}} \mathrm{V} / \mathrm{cm}\). The magnitude of the torque acting on the dipole is \(8 \sqrt{\alpha} \times 10^{-3} \mathrm{Nm}\), Where \(\alpha=\)___________ 2024 Hard
54. 54. Two charges of \(5 Q\) and \(-2 Q\) are situated at the points \((3 a, 0)\) and \((-5 a, 0)\) respectively. The electric flux through a sphere of radius \(4a\) having center at origin is 2024 Hard
55. 55. Two charges \(q\) and \(3 q\) are separated by a distance ' \(r\) ' in air. At a distance \(x\) from charge \(q\), the resultant electric field is zero. The value of \(x\) is _______. 2024 Hard
56. 56. Two identical conducting spheres \(\mathrm{P}\) and \(\mathrm{S}\) with charge \(Q\) on each, repel each other with a force \(16 \mathrm{~N}\). A third identical uncharged conducting sphere \(\mathrm{R}\) is successively brought in contact with the two spheres. The new force of repulsion between \(\mathrm{P}\) and \(\mathrm{S}\) is what? 2024 Hard
57. 57. A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are : 2023 Hard
58. 58. A cubical volume is bounded by the surfaces \(x =0, x = a , y =0, y = a , z =0, z = a\). The electric field in the region is given by \(\overrightarrow{ E }= E _0 \times \hat{ i }\). Where \(E _0=4 \times 10^4 NC ^{-1} m ^{-1}\). If \(a =2 cm\), the charge contained in the cubical volume is \(Q \times 10^{-14} C\). The value of \(Q\) is \(...........\) Take \(\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)\)  2023 Medium
59. 59. A point charge of \(10\,\mu C\) is placed at the origin. At what location on the \(X\)-axis should a point charge of \(40\,\mu\,C\) be placed so that the net electric field is zero at \(x =2\,cm\) on the \(X\)-axis ? 2023 Medium
60. 60. A point charge \(q_1=4 q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x =12\,cm\). Charge of proton is \(q_0\). The proton is placed on \(x\)-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is \(..........cm\). 2023 Medium
61. 61. A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\) 2023 Medium
62. 62. A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ........... 2023 Hard
63. 63. A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).
    2023 Hard
64. 64. An electron revolves around an infinite cylindrical wire having uniform linear change density \(2 \times 10^{-8}\,Cm ^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is \(.........\times 10^6\,ms ^{-1}\). Given mass of electron \(=9 \times 10^{-31}\,kg\)
    2023 Medium
65. 65. As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C\). The magnitude of charge within the cuboid is \(n \varepsilon_0 C\). The value of \(n\) is \(............\) (if dimension of cuboid is \(1 \times 2 \times 3 \;m ^3\) )
    2023 Medium
66. 66. As shown in the figure. a configuration of two equal point charges \(\left( q _0=+2 \mu C \right)\) is placed on an inclined plane. Mass of each point charge is \(20\,g\). Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \(h = x \times 10^{-3}\,m\) The value of \(x\) is \(..........\).(Take \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)\)
    2023 Hard
67. 67. Expression for an electric field is given by \(\vec{E}=4000 x^2 \hat{i} \frac{V}{m}\). The electric flux through the cube of side \(20\,cm\) when placed in electric field (as shown in the figure) is \(.........V cm\).
    2023 Medium
68. 68. Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) If an electric dipole of dipole moment \(30 \times 10^{-5}\,Cm\) is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason \(R\) : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below: 2023 Medium
69. 69. If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\). What will be the equivalent distance between charges in air for the same electrostatic force? 2023 Medium
70. 70. In a cuboid of dimension \(2 L \times 2 L \times L\), a charge \(q\) is placed at the centre of the surface ' \(S\) ' having area of \(4 L ^2\). The flux through the opposite surface to ' \(S\) ' is given by 2023 Medium
71. 71. Let \(\sigma\) be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region \(E_{ I }, E_{ II }\) and \(E_{III}\) are
    2023 Medium
72. 72. The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as 2023 Medium
73. 73. Three point charges \(q,-2 q\) and \(2 q\) are placed on \(x\)-axis at a distance \(x=0, x=\frac{3}{4} R\) and \(x=R\) respectively from origin as shown. If \(q =2 \times 10^{-6}\,C\) and \(R =2\,cm\), the magnitude of net force experienced by the charge \(-2 q\) is .......... \(N\)
    2023 Medium
74. 74. Two charges each of magnitude \(0.01\,C\) and separated by a distance of \(0.4\,mm\) constitute an electric dipole. If the dipole is placed in an uniform electric field ' \(\vec{E}\) ' of \(10\,dyne/C\) making \(30^{\circ}\) angle with \(\overrightarrow{ E }\), the magnitude of torque acting on dipole is : 2023 Easy
75. 75. Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\) 2023 Hard
76. 76. A charge of \(4\,\mu C\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be. 2022 Medium
77. 77. A long cylindrical volume contains a uniformly distributed charge of density \(\rho\). The radius of cylindrical volume is \(R\). A charge particle \((q)\) revolves around the cylinder in a circular path. The kinetic of the particle is 2022 Hard
78. 78. A long cylindrical volume contains a uniformly distributed charge of density \(\rho \;Cm ^{-3}\). The electric field inside the cylindrical volume at a distance \(x =\frac{2 \varepsilon_{0}}{\rho} m\) from its axis is \(.......Vm ^{-1}\)
    2022 Hard
79. 79. A positive charge particle of \(100 \,mg\) is thrown in opposite direction to a uniform electric field of strength \(1 \times 10^{5} \,NC ^{-1}\). If the charge on the particle is \(40 \,\mu C\) and the initial velocity is \(200 \,ms ^{-1}\), how much distance (in \(m\)) it will travel before coming to the rest momentarily 2022 Medium
80. 80. A spherically symmetric charge distribution is considered with charge density varying as \(\rho(r)=\left\{\begin{array}{ll}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { Zero } & \text { for } r>R\end{array}\right.\) Where, \(r ( r < R )\) is the distance from the centre \(O\) (as shown in figure). The electric field at point \(P\) will be.
    2022 Hard
81. 81. A uniform electric field \(E =(8\,m / e ) V / m\) is created between two parallel plates of length \(1 m\) as shown in figure, (where \(m =\) mass of electron and \(e=\) charge of electron). An electron enters the field symmetrically between the plates with a speed of \(2\,m / s\). The angle of the deviation \((\theta)\) of the path of the electron as it comes out of the field will be........
    2022 Hard
82. 82. A vertical electric field of magnitude \(4.9 \times 10^{5} N / C\) just prevents a water droplet of a mass \(0.1\, g\) from falling. The value of charge on the droplet will be  ........ \(\times 10^{-9} \;C\) \(\left(\right.\) Given \(\left.g =9.8 m / s ^{2}\right)\) 2022 Medium
83. 83. Given below are two statements Statement \(-I\) : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement \(-II\) : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below  2022 Medium
84. 84. If a charge \(q\) is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be
    2022 Medium
85. 85. In the figure, a very large plane sheet of positive charge is shown. \(P _{1}\) and \(P _{2}\) are two points at distance \(l\) and \(2 \,l\) from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields \(E_{1}\) and \(E_{2}\) at \(P _{1}\) and \(P _{2}\) respectively are
    2022 Medium
86. 86. The three charges \(q / 2, q\) and \(q / 2\) are placed at the corners \(A , B\) and \(C\) of a square of side ' \(a\) ' as shown in figure. The magnitude of electric field \((E)\) at the comer \(D\) of the square, is
    2022 Medium
87. 87. The volume charge density of a sphere of radius \(6 \,m\) is \(2 \,\mu cm ^{-3}\). The number of lines of force per unit surface area coming out from the surface of the sphere is \(....\times 10^{10}\, NC ^{-1}\).  [Given : Permittivity of vacuum  \(\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]\) 2022 Medium
88. 88. Three identical charged balls each of charge \(2 \,C\) are suspended from a common point \(P\) by silk threads of \(2 \,m\) each (as shown in figure). They form an equilateral triangle of side \(1 \,m\). The ratio of net force on a charged ball to the force between any two charged balls will be ...........
    2022 Hard
89. 89. Three point charges of magnitude \(5 \mu C , 0.16 \mu C\) and \(0.3 \mu C\) are located at the vertices \(A , B , C\) of a right angled triangle whose sides are \(AB =3\,cm\), \(BC =3 \sqrt{2}\,cm\) and \(CA =3\,cm\) and point \(A\) is the right angle corner. Charge at point \(A\) experiences \(N\) of electrostatic force due to the other two charges. 2022 Medium
90. 90. Two electric dipoles of dipole moments \(1.2 \times 10^{-30}\,cm\) and \(2.4 \times 10^{-30}\,cm\) are placed in two difference uniform electric fields of strengths \(5 \times 10^{4}\,NC ^{-1}\) and \(15 \times 10^{4}\,NC ^{-1}\) respectively. The ratio of maximum torque experienced by the electric dipoles will be \(\frac{1}{ x }\). The value of \(x\) is \(.....\) 2022 Medium
91. 91. Two identical charged particles each having a mass \(10 \,g\) and charge \(2.0 \times 10^{-7}\,C\) area placed on a horizontal table with a separation of \(L\) between then such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is \(0.25\), find the value of \(L\).[Use \(g =10\,ms ^{-2}\) ]..........\(cm\) 2022 Medium
92. 92. Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be. 2022 Medium
93. 93. Two identical positive charges \(Q\) each are fixed at a distance of ' \(2 a\) ' apart from each other. Another point charge qo with mass ' \(m\) ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \(q_{0}\) executes \(SHM\). The time period of oscillation of charge \(q_{0}\) will be. 2022 Hard
94. 94. Two point charges \(A\) and \(B\) of magnitude \(+8 \times 10^{-6}\,C\) and \(-8 \times 10^{-6}\,C\) respectively are placed at a distance \(d\) apart. The electric field at the middle point \(O\) between the charges is \(6.4 \times 10^{4}\,NC ^{-1}\). The distance ' \(d\) ' between the point charges \(A\) and \(B\) is..............\(m\) 2022 Medium
95. 95. Two point charges \(Q\) each are placed at a distance \(d\) apart. A third point charge \(q\) is placed at a distance \(x\) from mid-point on the perpendicular bisector. The value of \(x\) at which charge \(q\) will experience the maximum \(Coulomb's force\) is ............... 2022 Hard
96. 96. A body having specific charge \(8\,\mu {C} / {g}\) is resting on a frictionless plane at a distance \(10\, {cm}\) from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of \(100 \,{V} / {m}\) is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be \(....\, S.\)
    2021 Hard
97. 97. A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion? 2021 Medium
98. 98. A charge \('q'\) is placed at one corner of a cube as shown in figure. The flux of electrostatic field \(\overrightarrow{ E }\) through the shaded area is ...... .
    2021 Hard
99. 99. A cube is placed inside an electric field, \(\overrightarrow{{E}}=150\, {y}^{2}\, \hat{{j}}\). The side of the cube is \(0.5 \,{m}\) and is placed in the field as shown in the given figure. The charge inside the cube is \(.....\times 10^{-11} {C}\)
    2021 Hard
100. 100. A cube of side \('a'\) has point charges \(+Q\) located at each of its vertices except at the origin where the charge is \(- Q\). The electric field at the centre of cube is
     2021 Hard

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