flux associated with the cap of a sphere having semi vertical (semi-vertex) angle alpha and the charge Q is placed at centre is

Flux passing through the shaded surface of a sphere when a point charge q is placed at the center is (radius of the sphere is R)

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius alpha. (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surface?

In figure (a), a charge q is placed just outside the centre of a closed hemisphere. In figure (b), the same charge q is placed just inside the centre of the closed hemisphere and in figure (c), the charge is placed at the centre of hemisphere open from the base. Find the electric flux passing through the hemisphere in all the three cases.

A point charge +Q is placed at the centroid of an equilateral triangle. When a second charge +Q is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge is 8 N. The magnitude of the net force on the central charge when a third charge +Q is placed at another vertex of the triangle is

Six negative equal charge are placed at the vertical of a regular hexagon . 6q charge is placed at the centre of the hexagon . Find the electric dipole moment of the system.

A point charge is placed at the centre of spherical Gaussian surface. Is electric flux phi_(E) changed if (a) The sphere is replaced by a cube of same or different volume ? (b) The charge is moved off-centre in the original sphere, still remaining inside ? ( c ) The charge is moved just outside the original sphere ? (d) A second charge is placed near the outside to the origianl sphere ? (e) A second charge is placed inside the Gaussian surface ?

A point charge .Q. is placed at a point inside the cone as shown. The flux due to the charge through the curved surface is given as (2 Q)/(3 epsilon_(0)) . Now another charge .Q. is placed vertically above at the same distance from the base. The flux through the curved surface due to both charges is .

Q charge is uniformaly distributed over the same surface of a right circular cone of semi -vertical angle theta and height h The cone is uniformly rotated about its axis at angular velocity omega Calculated associated magnetic dipole moment .

Assertion : Five charges +q each are placed at five vertices of a regular pentagon. A sixth xharge -Q is placed at the centre of pentagon. Then, net electrostatic force on -Q is zero. Reason : Net electrostatic potential at the centre is zero.

A conducting sphere of radius b has a spherical cavity with its centre displaced by 'a' from centre of sphere O_(1) . A point charged q is placed at the centre of cavity O_(2) . Q charge is given to conducting sphere and charge q_(0) is placed at P, a distance c from centre O_(1) . Further O_(1), O_(2) and P are collinear