A charge Q is divided into two parts of q and Q-q. If the coulomb repulsion between them when they are seperated is to be maximum, the ratio of should be
1. 2
2. 1/2
3. 4
4. 1/4
An infinite number of charges, each of charge are placed on the x-axis with co-ordinates x= 1, 2, 4, 8, ......... If a charge of 1C is kept at the origin, that what is the net force acting on 1 charge
1. 9000 N
2. 12000 N
3. 24000 N
4. 36000 N
The region between two concentric spheres of radii 'a' and 'b' respectively (see figure), has volume charge density , where A is a constant and r is the distance from the centre. At the center of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is
1.
2.
3.
4.
A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACBD of the ring is
1. E along KO
2. 3E along OK
3. 3E along KO
4. E along OK
Consider an electric field , where is a constant. The flux through the shaded area (as shown in the figure)due to this field is
1.
2.
3.
4.
A charged ball B hangs from a silk thread S, which makes an angle with a large charged conducting sheet P, as shown in the figure. The surface change density of the sheet is proportional to
1. sin
2. tan
3. cos
4. cot
Consider, ; then
1. Only is an electrostatic
2. Only is electrostatic
3. Both are electrostatic
4. None of these
Two infinitely long parallel wires having linear charge densities respectively are placed at a distance of R meters. The force per unit length on either wire will be
1.
2.
3.
4.
Consider a uniform spherical charges distribution of radius centred at the origin O. In this distribution, a spherical cavity of radius , centred at P with distance OP=a= (see figure) is made. If the electric field inside the cavity of position , then the correct statement (s) is (are)
1. is uniform, its magnitude is independent of but its direction depends on
2. is uniform, its magnitude independs on and its direction depends on .
3. is uniform, its magnitude is independent of a but its direction depends on .
4. is uniform, and both its magnitude and direction depends on .
Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d<<l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constate rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them
1.
2.
3.
4.
A uniformly charged spherical shell of radius R carries uniform surface charged density of per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is the proportional to
1.
2.
3.
4.
A particle of mass M and charges q is at rest at the mid point between two other fixed similar changes each of magnitude Q placed a distance 2d apart. The system is collinear as shown in the figure. the particle is now displaced by a small amount x(x<<d) along the line joining the two charges and is left to itself. It will now oscillate about the mean position with a time period
1.
2.
3.
4.
A small sphere carrying a charge 'q' is hanging in between two parallel plates by a strring of length L. Time period of pendulum is . When a parallel plates are charged, the time period changes to T. The ratio is equal to
1.
2.
3.
4. None of these
Three charges are placed as shown in the figure. The x-component of the force on and proportional to
1.
2.
3.
4.
Two concentric conducting thin spherical shells A, and B, having radii are charged to and . The elctrical field along a line, (passing through the center is)
Two non-conducting spheres of radiiand carrying uniform charge densities , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlaping region
1. The electrostatic field is zero
2. The electrostatic potential is constant
3. The electrostatic field is constant in magnitude
4. The electrostatic field does not have same direction.
Two equal changes are seperated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when
1.
2.
3.
4.
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of with each other. When suspended in a liquid of density , the angle remains the same. If density of the material of the sphere is , the dielectric constant of the liquid is
1. 1
2. 4
3. 3
4. 2
Three infinity long charge sheets are placed as shown in figure. The electric field at point P is
1.
2.
3.
4.
A charged particle of mass m and charge q is released from rest in a uniform electric field E. Neglecting the effect of gravity, the kinetic energy of the charged particle after 't' second is
1.
2.
3.
4.
Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2, and 3 of radii R/2, R and 2R respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2, and 3 are respectively then,
1.
2.
3.
4.