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A solid sphere of radius R has a charge Q distributed in its volume with a charge density `rho = k r^a`, where k and a are constants and r is the distance from its centre. If the electric field at `r = R/2` is `1/8`. times that at `r = R,` find the value of
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The spatial distribution of electric field due to charges (A, B) is shown in figure. Which one of the following statements is correct
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A small sphere carrying a charge q' is hanging in between two parallel plates by a string of length L. Time period of pendulum is `T_o`. When parallel plates are charged, the time period changes to T. The ratio T/`T_o` is equal
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In a medium of dielectric constant K, the electric field is E. If `in_o` is permittivity of the free space, the electric displacement vector
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Three charges `-q_1, +q_2, and -q_3`, are R placed as shown in the figure. The x - component of the force on `-q_1`,
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An oil drop of radius r and density `rho` is held stationary in a uniform vertically upwards electric field 'E'. If `rho_0 (< rho)` is the density of air and e is quanta of charge, then the drop
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A surface has the area vector `vecA= (2hati + 3hatj)m^2`. The flux of an electric field through itifthe field is `vecE=-4hati V/m`
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Two small similar metal spheres A and B having charges 4q and – 4q, when placed at a certain distance apart, exert an electric force F on each other. When another identical uncharged sphere C, first touched with Athen with B and then removed to infinity, the force of interaction between A and B for the same separation will
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A square surface of side L. meter in the plane of the paper is placed in a uniform electric field `E ('volt'/m)` acting along the same plane at an angle `theta` with the - horizontal side of the square as shown in Figure. The electric flux linked to
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Two point dipoles of dipole moment `vecp_1 and vecp_2`. are at a distance x from each other and `vecp_1`||`vecp_2`. The force between the dipoles is
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In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will
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A particle of mass m and charge q is placed r at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y
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A positive charge +Q is fixed at a point A. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u as shown in the figure. The point B is at the large distance from A and at distance d from the line AC. The initial velocity is parallel to the line AC. The point C is at very large distance from A. The minimum distance (in meter) of +q from +Q during the motion is `d (1+sqrtA)`. Find the value of A. [Take `Qq= 4πε_0 mu^2d and d=(sqrt2-1)`
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Which of the following is a wrong
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A square surface of side L metres is in the plane of uur the paper. A uniform electric field `vecE ('volt' /m)`, also in the plane of the paper, is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is
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A thin semi-circular ring of radius r has a positive charge q distributed uniformly overit. The net electric field `vecE` at the centre O
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Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge of an
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When a piece of polythene is rubbed with wool, a charge of `–2×10^(–7) C` is developed on polythene. What is the amount of mass, which is transferred to
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`10^(12) alpha` – particles (Nuclei of helium) per second falls on a neutral sphere, calculate time in which sphere gets charged by
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If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between
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