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question_answer1) A flat plate with dimensions\[4cm\times 6cm\]is set with its plane at \[37{}^\circ \]to a uniform electric field\[\vec{E}=600\hat{j}N/C\], as shown below. What is the flux \[(inN{{m}^{2}}/C)\] through the plate?
question_answer2) A charge Q is uniformly distributed over a large plastic plate. The electric field at a point P close to the centre of the plate is 10 V/m. If the plastic plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q, the electric field (in V/m) at the point P will become ?
question_answer3) Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10 cm surrounding the total charge is\[25\text{ }V-m\]. The flux \[(in\text{ }V-m)\] over a concentric sphere of radius 20 cm will be ?
question_answer4) Electric flux through a surface of area\[100{{m}^{2}}\]lying in the \[xy\]plane is\[(in\text{ }V-m)\] if \[\vec{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}\].
question_answer5) Figure shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. Point P lies on a line connecting the centres of the spheres, at radial distance R/2 from the centre of sphere 1. If the net electric field at point P is zero and \[{{Q}_{1}}\]is \[64\mu C\], what is \[{{Q}_{2}}\]\[(in\mu C)\]
question_answer6) A large solid insulating sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre. A small particle with negative charge, initially at rest far from the sphere, approached it along the line of the tunnel, reaches its surface its surface with a speed v, and passes through the tunnel. Its speed at the centre of the sphere will be- (neglect all resistance forces & friction acting on particle except electrostatic force)
question_answer7) Outer cylinder of the coaxial nonconductor of radius 'b' is given a positive potential V relative to the inner cylinder of radius 'a' as shown in the figure (charge distribution is uniform). A charge q \[(mass=m)\] is set free with negligible velocity at the surface of the inner cylinder. Find the velocity (in m/s), when it hits the outer cylinder. [consider \[V=10,\text{ }q=-20,\text{ }m=1\]all in S.I. units]
question_answer8) A thick shell with inner radius R and outer radius 3R has uniform density\[\rho \,\,c/{{m}^{3}}\]. It has a spherical cavity of radius R as shown in the figure. The electric field at the centre O of the cavity is \[\frac{a\rho R}{{{12}_{{{\varepsilon }_{0}}}}}\] then the value of a is.
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