HARD
JEE Advanced
IMPORTANT
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Two concentric rings, one of radius a and the other of radius b, have the charges +q, and -2/5-3/2q, respectively, as shown in the figure. Find the ratio ba if a charged particle placed on the axis at z=a is in equilibrium
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Important Questions on Coulomb's Law and Electric Field

HARD
JEE Advanced
IMPORTANT
A rod AB of length L and mass m is uniformly charged with a charge Q, and it is suspended from the end A as shown in the figure. The rod can freely rotate about A in the plane of the figure. An electric field E is suddenly switched on in the horizontal direction due to which the rod gets turned by a maximum angle of 90°. The magnitude of E is equal to nMgQ. Find the value of n.
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HARD
JEE Advanced
IMPORTANT

Four charged particles each having charge Q=1 C are fixed at the corners of the base ( AB, C and D) of a square pyramid with slant length aAP=BP=PD=PC=a=2 m, a charge -Q is fixed at point P. A dipole with dipole moment p=1 C m is placed at the centre of the base and perpendicular to its plane as shown in figure. Force on the dipole due to the charge particles is x4πε0N. Find the value of x?

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HARD
JEE Advanced
IMPORTANT
A ring of radius R has charge -Q distributed uniformly over it. calculate the charge q that should be placed at the center of the ring such that the electric field becomes zero at a point on the axis of the ring distant R from the center of the ring. The value of q is Q4N. Find the value of N?
HARD
JEE Advanced
IMPORTANT
Two identical small equally charged conducting balls are suspended from long threads secured at one point. The charges and masses of the balls are such that they are in equilibrium when the distance between them is a (the length of the thread La). One of the balls is then discharged. Again for the certain value of distance bbl between the balls, the equilibrium is restored. Find the value of a3b3.
HARD
JEE Advanced
IMPORTANT

A particle having charge that of an electron and mass 1.6×10-30 kg is projected with an initial speed u at an angle 45o to the horizontal from the lower plate of a parallel plate capacitor as shown in the figure. The plates are sufficiently long and have separation 2 cm. The maximum value of velocity of particle not to hit the upper plate is W×106 m s-1. Take electric field between the plates as 103 V m-1 directed upward. Find the W.

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HARD
JEE Advanced
IMPORTANT
Excess electrons are placed on a small lead sphere of mass 6.90 g so that its net charge is -3.20×10-9 C. The number of excess electrons on the sphere is x×1010. Write the value of x.
HARD
JEE Advanced
IMPORTANT

In the figure shown, find the ratio of the linear charge densities λ1 (on semi – infinite straight wire) and λ2 (on semi – circular part) that is λ1/λ2 so that the field at O is along y direction.
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HARD
JEE Advanced
IMPORTANT
Two small metal spheres having equal charge and mass are suspended from same point on the ceiling of a damp room with silk threads of equal length. Let centre to centre distance between sphere be x, xl, l is length of silk thread. Due to ionization of medium, charge leaks off from each sphere and they keep on coming closer to each other at a constant rate. Let their approach velocity v varies as vx-12. If mass of each sphere is m then the rate at which charge varies with respect to time is dqdtN22πε0mgl. Find the value of N.