The Self Potential Energy of Continuous Charge Distributions

Q.

a metal sphere of radius 5 cm is charged such that the potential on its surface is 10 v . What is potential at centre of sphere?

Q. 8.Three concentric spherical shells have radii a, b, and c(a < b < c) and have surface charge densities , and respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have : (1) VC = VB = VA (2) VC = VA ≠ VB (3) VC = VB ≠ VA (4) VC ≠ VB ≠ VA

Q.

Q. Eight identical spherical drops, each carrying a charge 1 nC are at a potential of 900 V each. All these drops combine together to form a single large drop. Calculate the potential of this large drop. (Assume no wastage of any kind and take the capacitance of a sphere of radius r as proportional to r).

Q. A particle A having a charge of 5*10 raise to the power -7 C is fixed in a vertical wall. A second particle B of mass 100g and having equal charge is suspended by a silk thread of length 30 cm from the wall. The point of suspension is 30 cm above the particle A. Find the angle of the thread with the vertical when it says in equilibrium

Q. ntA thick shell with inner radius R and outer radius 3R has a uniform charge density sigma c/cm2 . I has a spherical cavity of radius R . The electric field at the center of cavityn ntn

Q. 47.A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d . The inner shell has total charge +2q and outer shell has charge +4q. Calculate the electric field in terms of q and r from common centre of two shells for

Q. charge Q, 2Q and -Q are given to three concentric conducting spherical shells P, Q and R respectively as shown in figure.The ratio of magnitude of charges on the inner and outer surface of shell R is

Q. Two concentric spherical conduting shells of radius R_1 and R_{2 } (R_1>R_2) are having uniformly distributed charges Q_1 and Q_2 respectively. the total energy of the system is

Q. 8.How much work is done to assemble eight identical point charges each of magnitude q at the corners of a cube of side a?

Q. 32.A point charge Q is placed at a distance R/2 from the of an uncharged conducting spherical shell of radius R then electric potential at center of shell is

Q.

A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

Q. A cylindrical capacitor has two co-axial cylindersof length 20 cm and radii 2r and r. Inner cylinderis given a charge 10 uC and outer cylinder acharge of-10 μ C. The potential difference betweenthe two cylinders will beIn 24πε oIn 201th SmV (2)(1) 4πε 0m V0.01 In 210 In 24πε 0m V(3)(4)4πε 0

Q. 34.Thin spherical conductor shell of radius R has a charge q. Another charge Q is placed at centre of the shell. The ectrostatic potential at a point P at a dist R/2 from the center of the shell is

Q. There are two concentric conducting spherical shells of radii 10cm and 20cm.The outer shell is charged to a potential of 50esu while the inner shell is earthed .The charge on the outer shell is 1)1000esu 2)2000esu 3)5esu 4)1500e

Q.
Find out the electric field intensity between the two long charged plates shown in the figure? ($\sigma$ - Surface charge density)


​​​​​​​$[$1 Mark$]$

1. $\frac{\sigma }{2{ϵ}_0}$
2. $\frac{\sigma }{{ϵ}_0}$
3. Zero
4. $\frac{3\sigma }{2{ϵ}_0}$

Q.

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m². (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?

Q. For two conducting concentric spherical shells of radius R1 and R2 respectively with charges Q1 and Q2 respectively find the a)the potential at the common centre b)potential difference between the two spherical shells

Q. a flexible spherical shell.of radius r with uniformly distributed charge q is expanded to radius 2r. the work.done by the electric force in this process

Q. A ring of radius r is kept vertical and a dipole[of charges q and distance l] is kept at the centre of the ring and perpendicular to the diameter of the ring. The ring is positively charged uniformly. Find the potential of the dipole at a distance X from the centre of the ring and along the axial line of the dipole.

Q. There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to

1. 
2. 
3. 
4. 

Q. An infinitely long solid cylinder of radius r has a uniform volume charge density rho. Magnitude of the electric field at point p which is at a distance r/2 from the axis of the cylinder

Q. Two concentric spherical shells of radii a and 1.2a have charges +Q and -2Q respectively .At what distance from centres the numerical value of potential will be same as that of centre?

Q. Find the electrostatic energy stored in a cylindrical shell of length $l$, inner radius $a$ and outer radius $b$, coaxial with a uniformly charged wire with linear charge density $\lambda$.

1. $U=\frac{{\lambda }^{2}l}{8\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$
2. $U=\frac{{\lambda }^{2}l}{2\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$
3. $U=\frac{{\lambda }^{2}l}{4\pi {\epsilon }_0}\log \left(\frac{a}{b}\right)$
4. $U=\frac{{\lambda }^{2}l}{4\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$

Q. A long cylindrical volume contains a uniformly distributed charge of density $\mathrm{\rho }$. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (figure 30-E5).

Q.

A large conducting plane has a surface charge density $1.0\times {10}^{-4}C{m}^{-2.}$ Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

Q. One thousand similar electrified raindrops merge into one bigger drop , so that their total charge remains unchanged. Find the total electrostatic energy of the bigger drop, assuming that the drops are spherical and that small drops are at large distances from one another.

1. Increases by $50$ times
2. Decreases by $50$ times
3. Increases by $100$ times
4. Decreases by $100$ times

Q. A spherical conducting thin shell of radius R given charge q .find its total energy

Q.

Two spheres of radii $12\mathrm{cm}$ and $16\mathrm{cm}$ have equal charges.The ratio of their energies is :

Q. A solid conducting sphere having charge Q is surrounded by an uncharged concentric conducting hollow spherical shell . Let the potential difference between the surface of the solid sphere and the hollow sphere be V . The shell is now given a charge -3Q , what is the new potential differened?

Q. a cylindrical capacitor has 2 co axial cylinders of length 20 cm and radii 2r and r. Inner cylinder is given a charge of -10 micro coulumb. The potential difference between the 2 cylinders will b