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question_answer1) Two semicircular wires of radius 20 cm and 10 cm have a common centre at the origin O as shown in the figure. Assume that both the wires are uniformly charged and have an equal charge of 0.70 nC each. The magnitude of electric field \[(in\,\,V{{m}^{-1}})\] at the common centre of curvature O of the system is
question_answer2) Three point charges \[{{Q}_{1}},{{Q}_{2}},{{Q}_{3}}\] in the order are placed equally spaced along a straight line. \[{{Q}_{2}}\] and \[{{Q}_{3}}\] are equal in magnitude but opposite in sign. If the net force on \[{{Q}_{3}}\] is zero, the value of \[{{Q}_{1}}\] is \[x({{Q}_{3}})\]. Find the value of x.
question_answer3) A uniformly charged conducting sphere of 4.4 m diameter has a surface charge density of 60 \[\mu C{{m}^{-2}}.\] The charge (in coulomb) in coulomb on the sphere is
question_answer4) When an electric dipole \[\overrightarrow{P}\] is placed in a uniform electric field \[\overrightarrow{E}\] then at what angle between \[\overrightarrow{P}\]and \[\overrightarrow{E}\] the value of torque will be maximum?
question_answer5) An uniform electric field E exists along positive x-axis. The work done in moving a charge 0.5 C through a distance 2 m along a direction making an angle \[60{}^\circ \] with x-axis is 10 J. Then the magnitude of electric field \[(in\,\,V{{m}^{-1}})\] is
question_answer6) Two point charges \[+3\mu C\] and \[+8\mu C\] repel each other with a force of 40N. If a charge of \[-5\mu C\] is added to each of them then the force (in newton) between them will become
question_answer7) Two equally charged identical metal spheres A and B repel each other with a force\[2.0\times {{10}^{-5}}N\]. Another identical uncharged sphere C is touched to A and then placed at the midpoint between A and B. What is the net electric force (in newton) on C?
question_answer8) A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the center. What is the ratio of the magnitude of the electric field at a distance 2R from the center to the magnitude of the electric field at a distance of R/2 from the center?
question_answer9) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field of\[100\text{ }V{{m}^{-1}}\]. If the mass of the drop is\[1.6\text{ }\times \text{ }{{10}^{-3}}g\], the number of electrons carried by the drop is \[(g=10m{{s}^{-2}})\]
question_answer10) An electric dipole is placed at an angle of \[30{}^\circ \] with an electric field of intensity\[2\text{ }\times \text{ }{{10}^{5}}\text{ }N{{C}^{-1}}\], It experiences a torque of 4 Nm. Calculate the charge (in mC) on the dipole if the dipole length is 2 cm.
question_answer11) A point charge of charge q and mass m is placed at rest at point X at distance r from a short electric dipole. The initial acceleration of charge \[a=\frac{k.q.p}{2m{{r}^{3}}}n,\] where \[k=\frac{1}{4\pi {{\varepsilon }_{0}}}.\] Then n is
question_answer12) A solid sphere of radius R has a charge Q distributed in its volume with a charge density \[\rho =\kappa \,{{r}^{a}}\], where \[\kappa \] and a are constants and r is the distance from its centre. If the electric field at \[r=\frac{R}{2}\] is \[=\frac{1}{8}\] times that at \[r=R\], find the value of a.
question_answer13) A charge of \[10\mu C\] is placed at the centre of a hemisphere of radius \[R=10cm\] as shown. The electric flux through the hemisphere (in MKS units) is
question_answer14) A point charge causes an electric flux of\[-1.0\times {{10}^{3}}N{{m}^{2}}/C\] to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge of the radius of the Gaussian surface were three times, how much flux would pass through the surface.
question_answer15) An electric field of 1000 V/m is applied to an electric dipole at an angle of\[45{}^\circ \]. The value of electric dipole moment is\[{{10}^{-29}}C.m\]. What is the potential energy (in joule) of the electric dipole?
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charge \[a=\frac{k.q.p}{2m{{r}^{3}}}n,\] where \[k=\frac{1}{4\pi {{\varepsilon }_{0}}}.\] Then n is 
