Electrostatic Potential and Capacitance

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.21 Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively.

(a) What is the electrostatic potential at the points (0, 0, z) and (x, y, 0) ?

(b) Obtain the dependence of potential on the distance r of a point from the origin when r/a >> 1.

(c) How much work is done in moving a small test charge from the point (5,0,0) to (–7,0,0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

9 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.21 Charge –q is located at (0,0,-a) and charge +q is located at (0,0,a). Hence, they form a dipole. Point (0,0,z) is on the axis of this dipole and point (x,y,0) is normal to the axis of the dipole. Hence electrostatic potential at point (x,y,0) is zero. Electrostatic potential at point (0,0,z) is

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.20 Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

14 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.20 For Sphere A: We assume, radius = a, Charge on the sphere = $Q_{A}$ , Capacitance = $C_{A}$ , Electric field = $E_{A}$

For Sphere B: We assume, radius = b, Charge on the sphere = $Q_{B}$ , Capacitance = $C_{B}$ , Electric field = $E_{B}$

$E_{A} i s g i v e n b y, E_{A} =$ $\frac{Q_{A}}{4 π ε_{0} a^{2}}$ and $E_{B} i s g i v e n b y, E_{B} =$ $\frac{Q_{B}}{4 π ε_{0} b^{2}}$

$\frac{E_{A}}{E_{B}}$ = $\frac{Q_{A}}{Q_{B}} \times \frac{b^{2}}{a^{2}}$ ……….(

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.19 If one of the two electrons of a $H_{2}$ molecule is removed, we get a hydrogen molecular ion $H_{2}^{+}$ . In the ground state of an $H_{2}^{+}$ , the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

9 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.19

Let the charge in Proton 1 be $q_{1}$ = 1.6 $\times 10^{- 19}$ C, in Proton 2, $q_{2}$ = 1.6 $\times 10^{- 19}$ C and the charge in the electron, $q_{3}$ = $-$ 1.6 $\times 10^{- 19}$ C

Distance between Proton 1 & Proton 2, $d_{1}$ = 1.5 Å = 1.5 $\times 10^{- 10}$ m

Distance between Proton 1 and Electron,

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.18 In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:

(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton.

(b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

(c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 Å separations?

8 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.18 The distance between electron – proton of a hydrogen atom, d = 0.53 Å = 0.53 $\times 10^{- 10}$ m

Charge of an electron, $q_{1}$ = $-$ 1.6 $\times 10^{- 19}$ C

Charge of a proton, $q_{2}$ = 1.6 $\times 10^{- 19}$ C

Potential at infinity = 0

Potential energy of the system = Potential energy at infinity – Poten

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.17 A long charged cylinder of linear charged density $λ$ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

8 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.17

Let charge density of the long charged cylinder, with length L and radius r be $λ .$

Another cylinder of same length surrounds the previous cylinder with radius R.

Let E be the electric field produced in the space between the two cylinders.

Electric flux through the Gaussian surface is given by Gau

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New answer posted•a year ago

Electrostatic Potential and Capacitance Class 12th

2.15 A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.

(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

7 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

2.15 Charge placed at the centre of the shell is +q. Hence a charge of magnitude of –q will be induced to the inner surface of the shell. Therefore, the total charge on the inner surface of the shell is –q.

Surface charge density at the inner surface of the shell is given by the relation,

$σ_{1} = \frac{T o t a l c h a r g e}{I n n e r s u r f a c e a r e a} = \frac{- q}{4 π r_{1}^{2}}$ …………(1