Electrostatics

In a uniformly charged sphere of total charge \(Q\) and radius \(R,\) the electric field \(E\) is plotted as function of distance from the center. The graph which would correspond to the above will be:

The electrostatic potential inside a charged spherical ball is given by \(\phi = a{r^2} + b\) where \(r\) is the distance from the center and \(a,b\) are constants. Then the charge density inside the ball is:

Two identical charged spheres suspended from a common point by two massless strings of length \(l\) are initially a distance \(d\left( {d < < 1} \right)\) apart because of their mutual repulsion. The charge begins to leak from both the sph...

Let there be a spherically symmetric charge distribution with charge density varying as \(\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)\) upto \(r=R,\) and \(\rho \left( r \right) = 0\) for \(r>R,\) where \(r\)...

A thin semi-circular ring of radius \(r\) has a positive charges \(q\) distributed uniformly over it. The net field \(\overrightarrow E\) at the center \(O\) is

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of \({30^ \circ }\) with each other. When suspended in a liquid of density \(0.8g\) \(c{m^{ - 3}},\) the angle remains the same. If density o...

Two points \(P\) and \(Q\) are maintained at the potentials of \(10\) \(V\) and \(-4\) \(V\), respectively. The work done in moving \(100\) electrons from \(P\) to \(Q\) is :

Let \(P\left( r \right) = {Q \over {\pi {R^4}}}r\) be the change density distribution for a solid sphere of radius \(R\) and total charge \(Q\). For a point \('p'\) inside the sphere at distance \({r_1}\) from the center of the sphere, the ...

A charge \(Q\) is placed at each of the opposite corners of a square. A charge \(q\) is placed at each of the other two corners. If the net electrical force on \(Q\) is zero, then \(Q/q\) equals:

(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)
Statement-1 : For a charged particle moving from point \(P\) to point \(Q\), the ne...

A thin spherical shell of radius \(R\) has charge \(Q\) spread uniformly over its surface. Which of the following graphs most closely represents the electric field \(E(r)\) produced by the shell in the range \(0 \le r < \infty ,\) where $$r...

Charges are placed on the vertices of a square as shown. Let \(\overrightarrow E\) be the electric field and \(V\) the potential at the center. If the charges on \(A\) and \(B\) are interchanged with those on \(D\) and \(C\) respectively, ...

An electric charge \({10^{ - 3}}\,\,\mu \,C\) is placed at the origin \((0,0)\) of \(X-Y\) co-ordinate system. Two points \(A\) and \(B\) are situated at \(\left( {\sqrt 2 ,\sqrt 2 } \right)\) and \(\left( {2,0} \right)\) respectively. The...

The potential at a point \(x\) (measured in \(\mu \,m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = 20/\left( {{x^2} - 4} \right)\) volt
The electric field \(E\) at \(x = 4\,\mu \,m\) is given by

Two insulating plates are both uniformly charged in such a way that the potential difference between them is \({V_2} - {V_1} = 20\,V.\) (i.e., plate \(2\) is at a higher potential). The plates are separated by \(d=0.1\) \(m\) and can be tre...

An electric dipole is placed at an angle of \({30^ \circ }\) to a non-uniform electric field. The dipole will experience

Two spherical conductors \(A\) and \(B\) of radii \(1\) \(mm\) and \(2\) \(mm\) are separated by a distance of \(5\) \(cm\) and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the rati...

Two point charges \(+8q\) and \(-2q\) are located at \(x=0\) and \(x=L\) respectively. The location of a point on the \(x\) axis at which the net electric field due to these two point charges is zero is

A charged ball \(B\) hangs from a silk thread \(S,\) which makes angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to
f

Two thin wire rings each having a radius \(R\) are placed at a distance \(d\) apart with their axes coinciding. The charges on the two rings are \(+q\) and \(-q.\) The potential difference between the centres of the two rings is

A charge particle \('q'\) is shot towards another charged particle \('Q'\) which is fixed, with a speed \('v'\). It approaches \('Q'\) upto a closest distance \(r\) and then returns. If \(q\) were given a speed of \('2v'\) the closest dista...

Four charges equal to -\(Q\) are placed at the four corners of a square and a charge \(q\) is at its center. If the system is in equilibrium the value of \(q\) is

Two spherical conductors \(B\) and \(C\) having equal radii and carrying equal charges on them repel each other with a force \(F\) when kept apart at some distance. A third spherical conductor having same radius as that \(B\) but uncharged ...

A charged oil drop is suspended in a uniform field of \(3 \times {10^4}\) \(v/m\) so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge \(= 9.9 \times {10^{ - 15}}\,\,kg\) and \(g = 10\,m/{s^2}\))...

If the electric flux entering and leaving an enclosed surface respectively is \({\phi _1}\) and \({\phi _2},\) the electric charge inside the surface will be

A thin spherical conducting shell of radius \(R\) has a charge \(q.\) Another charge \(Q\) is placed at the center of the shell. The electrostatic potential at a point \(P\) a distance \({R \over 2}\) from the center of the shell is

Three charges \(- {q_1}, + {q_2}\) and \(- {q_3}\) are placed as shown in the figure. The \(x\)-component of the force on \(- {q_1}\) is proportional to

If a charge \(q\) is placed at the center of the line joining two equal charges \(Q\) such that the system is in equilibrium then the value of \(q\) is

A charged particle \(q\) is placed at the centre \(O\) of cube of length \(L(ABCDEFGH).\) Another same charge \(q\) is placed at a distance \(L\) from \(O\). Then the electric flux through \(ABCD\) is

On moving a charge of \(20\) coulomb by \(2\) \(cm,\) \(2\) \(J\) of work is done, then the potential differences between the points is