The minimum strength of a uniform electric field which can tear a conducting uncharged thin-walled sphere into two parts is known to be `E_(0)`. Determine the minimum electric field strength `E_(1)` required to tear the sphere of twice as large radius if the thickness ofits walls is the same as in the former case.

Near an infinitely large flat plate with a surface charge density o on each side, the field strength is** E=delta/(in n^delta), while the field produced by a point charge at a distance r frorn the chargo is Prove that for a uniformly charged disk with a surface charge density a (on each side), the electric field strength on the axis of the disk is the same as for an infinitely large flat plate if the distances arc small in comparison with the disk's radius R, and is the same as for a point charge if the distances are large ** Usually the value of the field strength given in textbooks is half the one given here, since there it is assumed that the charge is on a geometric plane

A uniform electric field in positive x -direction on exists in space. An uncharged solid conducting sphere is now placed in region of this uniform electric field. The centre of this sphere of radius R lies at origin. Then electric potential at any point on y-z plane (i.e. x=0 plane) due to only induced charged on surface of sphere.

Two concentric conducting thin shells of radius R and 2 R carry charges +Q and +3Q respectively. The magnitude of electric field at a distance x outside and inside from the surface of outer sphere is same. Then the value of x is

A hollow spherical conductor of radius R has a charge Q on it. A small dent on the surface decreases the volume of the spherical conductor by 2%. Assume that the charge density on the surface does not change due to the dent and the electric field in the dent region remains same as other points on the surface. (a) Delta E is the electrostatic energy stored in the electric field in the shallow dent region and E is the total electrostatic energy of the spherical shell. Find the ratio (Delta E)/(E) (b) Using the ratio obtained in part (a) calculate the percentage change in capacitance of the sphere due to the dent.

If x is measured from the centre of uniformly charged non-conducting sphere and a is radius of sphere the graph which best represents the variation of electric field (E) with x is E o a E

A hollow charged sphere of radius R has a constant surface charge density o. Of the following graphs the one, which shows the variation of the electric field strength E with distance X from the centre of the sphere is (A) E I=R x (B) E 1

An electron accelerated by a potential difference V= 3 volt first enters into a uniform electric field of a parallel plate capacitor whose plates extend over a length l= 6 cm in the direction of initial velocity. The electric field is normal to the direction of initial velocity and its strength varies with time as E= alpha t, where alpha= 3600 V m^-1 s^-1. Then the electron enters into a uniform magnetic field of induction B = pi xx 10^-9 T. Direction of magnetic field is same as that of the electric field. Calculate pitch of helical path traced by the electron in the magnetic field. (Mass of electron, m = 9 xx 10^-31 kg )

Two large thin conducting plates with a small gap in between are placed in a uniform electric field E (perpendicular to the plates.)The area of each plate is A, and charges +Q and -Q are given to these plates as shown in figure. If R,S, and T are three points in space, then the