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question_answer1) The electric field strength depends only on the x, y and z coordinates according to the law\[E=\frac{a\left( x\hat{i}+y\hat{j}+z\hat{k} \right)}{{{\left( {{x}^{2}}+{{y}^{2}}+{{z}^{2}} \right)}^{{3}/{2}\;}}}\], where\[a=122.5\]SI unit and is a constant. Find the potential difference (in volt) between (3, 2, 6) and (0, 3, 4).
question_answer2) Two spherical bobs of same mass and radius having equal charges are suspended from the same point by strings of same length. The bobs are immersed in a liquid of relative permittivity \[{{\in }_{r}}\]and density\[{{\rho }_{o}}\]. Find the density \[\rho \] of the bob in \[g/c{{m}^{3}}\]for which the angle of divergence of the strings to be the same in the air and in the liquid\[\left( {{\varepsilon }_{r}}=3,{{\rho }_{0}}=2g/c{{m}^{3}} \right)\]?
question_answer3) An inclined plane makes an angle of \[30{}^\circ \]with the horizontal electric field E of 100 V/m. A particle of mass 1 kg and charge 0.01 C slides down from a height of 1 m. If the coefficient of friction is 0.2, find the time taken for the particle to reach the bottom. (in sec)
question_answer4) A particle of mass m carrying charge 'q' is projected with velocity (v) from point P towards an infinite line charge from a distance 'a'. Its speed reduces to zero momentarily at point Q which is at a distance a/2 from the line charge. If another particle with mass m and charge \[-q\]is projected with the same velocity v from point P towards the line charge. Its speed is found to be \[\frac{Nv}{\sqrt{2}}\]at point 'Q'. Find the value of N.
question_answer5) A thread carrying a charge (uniform) \[\lambda \]per unit length has configuration shown in figure. Assuming a curvature radius R to be considerably less than the length of thread. Find the magnitude of electric field strength at point O.
question_answer6) The angle of \[\vec{E}\]at point P due to uniformly charged finite rod will be \[\frac{\pi }{a}\]radian, with x axis then value of a is-
question_answer7) Find the force in N experienced by the semicircular rod of radius R charged with a charge q, placed as shown in figure. The line of charge with linear charge density \[\lambda \]is passing through its centre and perpendicular to the plane of rod(\[q=2{{\pi }^{2}}{{\varepsilon }_{0}}c,R=1\text{ }metre,\lambda =2C/m)\]
question_answer8) A block of mass m containing a net positive charge q is placed on a smooth horizontal table which terminated in a vertical wall as shown in figure. The distance of the block from the wall is d. A horizontal electric field E towards right is switched on. Assuming elastic collisions (if any) find the time period of the resulting oscillatory motion in second.\[\left( \frac{q}{m}=1C/kg,E=1\frac{N}{C},d=2m \right)?\]
question_answer9) The charge \[Q=\pi C\]is distributed on a thin semicircular ring of radius\[R=2m\]. There is a uniform electrostatic field \[\left| {\vec{E}} \right|=2N/C\]directed horizontal. The semicircular ring can rotate freely about a fixed vertical axis AB. Initially the ring is in static equilibrium a shown in figure. If we want to rotate it about the fixed axis by \[90{}^\circ \]then minimum work required on the ring is xJ. Find the value of x.
question_answer10) A long cylindrical wire carries a positive charge of linear density\[2.0\times {{10}^{-8}}C/m\]. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. If it is\[a\times 1.44\times {{10}^{-17}}Joule\]. then a is?
question_answer11) Two circular rings A and B, each of radius\[a=30cm\]are placed coaxially with their axes horizontal in a uniform electric field \[E={{10}^{5}}N/C\]directed vertically upward as shown in figure. Distance between centres of these rings A and B is\[h=40cm\]. Ring A has a positive charge \[{{q}_{1}}=10\mu C\]while ring B has a negative charge of magnitude\[{{q}_{2}}=20\mu C\], A particle of mass\[m=100\text{ }g\]and carrying a positive charge \[q=10\mu C\]is released from rest at the centre of the ring A. Calculate its velocity when it has moved a distance of\[40cm\]. (Take \[g=10m{{s}^{-2}}\]) if it is v m/s. Find \[v/\sqrt{2}\].
question_answer12) In the figure shown S is a large non-conducting sheet of uniform charge density\[\sigma \]. A rod R of length ℓ and mass ?m? is parallel to the sheet and hinged at its mid point. The linear charge densities on the upper and lower half of the rod are shown in the figure. Find the angular acceleration of the rod just after it is released. If it is \[\frac{a\sigma \lambda }{2{{m}_{{{\varepsilon }_{0}}}}}\].Find a.
question_answer13) Small identical balls with equal charges are fixed at vertices of regular polygon with side a. At a certain instant, one of the balls is released & a sufficiently long time interval later, the ball adjacent to the first released ball is freed. The kinetic energies of the released balls are found to differ by K at a sufficiently long distance from the polygon. Determine the charge q of each ball. If it is\[\frac{1}{a}\times {{10}^{-4}}C\]. Find a. (\[k=10\text{ }Joule\], side length\[=1m\])
question_answer14) The electric potential in a region is given by\[V(x,\text{ }y,\text{ }z)\] =\[a{{x}^{2}}+a{{y}^{2}}+ab{{z}^{2}}\], 'a' is a positive constant of appropriate dimensions and b, a positive constant such that V is volts when x, y, z are in m. Let\[b=2\]. The work done by the electric field when a point charge\[+4\mu C\]moves from the point (0, 0, 0, 1m) to the origin is\[50\mu J\]. The radius of the circle of the equipotential curve corresponding to \[V=6250\text{ }volts\]and \[z=\sqrt{2}\]m is \[\alpha \]m. Find\[{{\alpha }^{2}}\].
question_answer15) A particle having mass m and charge \[(-q)\] moves along an ellipse around a fixed charge Q such that its maximum and minimum distance from the fixed charge are \[{{r}_{1}}\] and \[{{r}_{2}}\]respectively. Show that the angular momentum L of this particle about Q is \[a\times {{10}^{4}}Ns\], then find a. \[(Q=2C,\text{ }q=1C,\,\,{{r}_{1}}=3m,\,\,{{r}_{2}}=1m,\text{ }m=0.3kg)\]
question_answer16) Two uniformly charged large plane sheets \[{{S}_{1}}\]and \[{{S}_{2}}\]having charge densities \[{{\sigma }_{1}}\] and \[{{\sigma }_{2}}({{\sigma }_{1}}>{{\sigma }_{2}})\]are placed at a distance d parallel to each other. A charge \[{{q}_{0}}\]is moved along a line of length a\[(a<d)\]at an angle \[45{}^\circ \]with the normal to\[{{S}_{1}}\]. Calculate the work done by the electric field, in joule\[({{q}_{0}}=2C,\,\,{{\sigma }_{1}}={{3}_{\varepsilon 0}}C/{{m}^{2}},\,\,{{\sigma }_{2}}={{\varepsilon }_{0}}C/{{m}^{2}},a=\sqrt{2}metre).\]
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Assuming a curvature radius R to be considerably less than the length of thread. Find the magnitude of electric field strength at point O. 
