Charge vs Potential in Spherical Conductor

Q. Two identical beads, each have a mass $m$ and charge $q$. When placed at a distance $R$ apart in a hemispherical bowl of radius $R$ with frictionless, non-conducting walls, the beads are at equilibrium as shown in figure. Determine the charge on each bead, if $m=0.001\text{kg}$ and $R=0.001\text{m}$

1. $2\times {10}^{-10}\text{C}$
2. $4\times {10}^{-10}\text{C}$
3. $6\times {10}^{-10}\text{C}$
4. $8\times {10}^{-10}\text{C}$

Q. Answer carefully: (a) Two large conducting spheres carrying charges Q1 and Q2 arebrought close to each other. Is the magnitude of electrostaticforce between them exactly given by Q1 Q2/4pe0r2, where r isthe distance between their centres? (b) If Coulomb’s law involved 1/r3 dependence (instead of 1/r2), would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in anelectrostatic field configuration. Will it travel along the fieldline passing through that point? (d) What is the work done by the field of a nucleus in a completecircular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surfaceof a charged conductor. Is electric potential also discontinuousthere? (f ) What meaning would you give to the capacitance of a singleconductor? (g) Guess a possible reason why water has a much greaterdielectric constant (= 80) than say, mica (= 6).

Q. The radii of two charged metal spheres are 5 cm and 10 cm both having same charge 75 mC. If they are connected by a wire, the quantity of charge transferred through the wire is

1. 25 mC
2. 50 mC
3. 75 mC
4. Zero

Q. two charges + q and + 2q, are held in place on the x axis at the locations x-d andx + d respectively. A third charge, +3q, is released from rest on the y axis at y d(a) Find the electric potential at the initial location of the third charge. (b) Find the initial electricpotential energy of the third charge. (c) What is the kinetic energy of the third charge when ithas moved infinitely far away from the other two charges?

Q. The capacitance of an isolated metallic sphere of radius $36\text{cm}$ will be

1. $40\text{pF}$
   
2. $20\text{pF}$
3. $80\text{pF}$
4. $10\text{pF}$

Q. electric potential energy due to a hollow charged sphere

Q. An electron (charge=-e) is placed at each of the 8 corners of a cube of side a and an alpha particle (charge=+2e) at the centre of the cube . Calculate the potential energy of the system .

Q. If two conducting spheres are separately charged and then brought in contact, then

1. The final potential is always the mean of the original potentials of the two spheres

2. The total energy of the two spheres is conserved

3. The total charge on the two spheres is conserved

4. Both the total energy and charge are conserved

Q. 114.Electric potential at a point, r distance away due to a point charge q at point A is V . If twice of this charge is distributed uniformly on the surface of a hollow sphere of radius 4r with centre at a point A the potential at a point now is

Q. two charged metallic spheres of radii r1 and r2 are touched and separated calculate the ratio of their 1 charges 2 potential 3 self energy 4 electric field at the surface 5 surface charge den

Q. A spherical capacitor has an inner sphere of radius 12 cm and anouter sphere of radius 13 cm. The outer sphere is earthed and theinner sphere is given a charge of 2.5 μC. The space between theconcentric spheres is filled with a liquid of dielectric constant 32. (a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere? (c) Compare the capacitance of this capacitor with that of anisolated sphere of radius 12 cm. Explain why the latter is muchsmaller.

Q. Answer the following: (a) The top of the atmosphere is at about 400 kV with respect tothe surface of the earth, corresponding to an electric field thatdecreases with altitude. Near the surface of the earth, the fieldis about 100 Vm–1. Why then do we not get an electric shock aswe step out of our house into the open? (Assume the house tobe a steel cage so there is no field inside!) (b) A man fixes outside his house one evening a two metre highinsulating slab carrying on its top a large aluminium sheet ofarea 1m2. Will he get an electric shock if he touches the metalsheet next morning? (c) The discharging current in the atmosphere due to the smallconductivity of air is known to be 1800 A on an average overthe globe. Why then does the atmosphere not discharge itselfcompletely in due course and become electrically neutral? Inother words, what keeps the atmosphere charged? (d) What are the forms of energy into which the electrical energyof the atmosphere is dissipated during a lightning?(Hint: The earth has an electric field of about 100 Vm–1 at itssurface in the downward direction, corresponding to a surfacecharge density = –10–9 C m–2. Due to the slight conductivity ofthe atmosphere up to about 50 km (beyond which it is goodconductor), about + 1800 C is pumped every second into theearth as a whole. The earth, however, does not get dischargedsince thunderstorms and lightning occurring continually allover the globe pump an equal amount of negative charge onthe earth.)

Q.

The insulated metal spheres of radii R₁ and R₂ having charges Q₁ and Q₂ respectively are connected to each other. There is

1. An increase in the energy of the system

2. No change in the energy of the system

3. Always a decrease in the energy of the system

4. A decrease in the energy of the system unless Q₁R₂=Q₂R₁

Q.

Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

Q. A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show that the capacitance of a spherical capacitor is given byC=4ϵ∏r1r2/r1-r2where r1 and r2 are the radii of outer and inner spheres, respectively.

Q.

If at $t=0$, switch $\text{S}$ is closed, then at steady state find the net charge that flows through the given circuit as shown

1. $500\mu \text{C}$
2. $800\mu \text{C}$
3. $300\mu \text{C}$
4. $400\mu \text{C}$

Q. Two point charges +5x10^(-6) C and -2x10^(-6) C are kept at a distance of 1m in free space. The distance between the two zero potential points on the line joining the charges is (a)2/7 m (b)2/3 m (c)22/21 m (d)20/21 m

Q. A system comprises of a solid non conducting sphere of charge $Q$ and radius $R$. A point charge $q$ is placed at a distance $r$ from the centre of sphere. Find the total energy of the system
$[k=\frac{1}{4\pi {\epsilon }_0}]$

1. $\frac{3k{Q}^2}{5R}+\frac{kQq}{r}$
2. $\frac{3k{Q}^2}{5R}$
3. $\frac{kQq}{r}$
4. $\frac{3k{Q}^2}{5R}+\frac{kQq}{R}$

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ having capacitances $4\mu \text{F}$ and $6\mu \text{F}$ are seperately charged upto $10\text{V}$ and $5\text{V}$ respectively. Now positive plate of $\text{A}$ is connected to the positive plate of $\text{B}$ and negative plate of $\text{A}$ is connected with negative plate of $\text{B}$. Find the final charge on each capacitor ?

1. $35\mu \text{C}$, $35\mu \text{C}$
2. $20\mu \text{C}$, $50\mu \text{C}$
3. $40\mu \text{C}$, $30\mu \text{C}$
4. $28\mu \text{C}$, $42\mu \text{C}$

Q. Two charged metal spheres A and B have radii in the ratio 2:3 with charges $5\times {10}^{-6}C$ and $10\times {10}^{-6}C$ respectively. If they are connected by a wire. Then

1. No charge flows between A and B

2. 1μC of charge flows from A to B till common potential is reached

   
   
3. 1μC of charge flows from B to A till common potential is reached

   
   

4. 5μC of charge flows from B to A till their charges are equal

Q.

Consider a solid hemisphere of radius R having charge Q/2. The electric potential at a point at a distance of R/2 from the centre of the sphere on the flat surface of hemisphere is

Q. two metal spheres of radii a and b are connected by a thin wire. their seperation is very large compared to their dimensions the capaci†an ce of this system i

Q. A spherical shell made of material of conductivity $\frac{{10}^9}{\pi }(\Omega -\text{m}{)}^{-1}$ has a thickness $t=2\text{mm}$ and radius of shell is $R=10\text{cm}$. In an arrangement, it's inside surface is kept at a lower potential with respect to its outer surface. The resistance offered by the shell is equal to:

1. $5\pi \times {10}^{-12}\Omega$
2. $2.5\times {10}^{-11}\Omega$
3. $5\times {10}^{-12}\Omega$
4. $5\times {10}^{-11}\Omega$

Q. Two charges –2μ C and +2μ C are placed on y-axis are separated by a dis†an ce `a (in cm). The magnitude of potential due to these charges at dis†an ce 100 m whose positition vector is at an angle 60^° from the y-axis is (centre of dipole is at origin)

Q. 8. Two metallic spheres are placed in a liquid of dielectric { constant a such that their centers are nearly 1 m apart. It is { given that radius of each sphere is 2cm and capacitance { of system of spheres is 10N farads. Find the value of {N .