Electric Charges and Fields
What is the S.I. unit of electric charge?
The number of electrons present in $1\text{ Coulomb}$ of negative charge is:
What is the dimensional formula of the permittivity of free space ($\ mepsilon_0$)?
An electric dipole of dipole moment $p$ is placed in a uniform electric field $E$. The maximum torque acting on the dipole is:
The ratio of electric field intensity at a distance $r$ on the axial line to that on the equatorial line for a short electric dipole is:
What is the S.I. unit of electric flux?
The electric field intensity inside a uniformly charged thin spherical shell is:
The magnitude of electric field intensity near an infinite thin plane sheet of uniform surface charge density $\sigma$ is:
The net electric flux emerging through a closed Gaussian surface enclosing an electric dipole is:
The dielectric constant ($K$) of a perfect metallic conductor is:
Two point charges of $+1\ \mu\text{C}$ and $-1\ \mu\text{C}$ are separated by a distance of $2\text{ cm}$. What is the magnitude of the electric dipole moment of this system?
The electric field intensity $E$ at a perpendicular distance $r$ from an infinitely long straight uniformly charged wire depends on $r$ as:
State the principle of quantization of electric charge.
State Coulomb's law in electrostatics and write its mathematical formula.
Why can two electric field lines never intersect each other? Explain.
Define electric dipole moment. Is it a scalar or a vector quantity? Mention its SI unit.
State Gauss's law in electrostatics and express it mathematically.
Write the formula for the torque acting on an electric dipole placed in a uniform electric field. Under what condition is this torque maximum?
Define electric field intensity at a point. Is it a scalar or vector quantity? Mention its SI unit.
What is the electric field intensity inside a uniformly charged thin spherical shell? Explain the reason using Gauss's law.
How many electrons must be removed from a neutral metallic sphere so that it acquires a positive charge of $1.6 \times 10^{-7}\text{ C}$?
State four important properties of electric field lines. Why can two electric field lines never cross each other?
Derive an expression for the torque acting on an electric dipole placed in a uniform electric field. Under what conditions is this torque maximum and minimum?
State Gauss's Law in electrostatics. Using Gauss's Law, derive the expression for the electric field intensity due to an infinitely long straight uniformly charged wire.
Define electric dipole moment. State its SI unit, direction, and write its physical significance.
State Gauss's Law in electrostatics. Mention any three important characteristics of a Gaussian surface.
State Coulomb's inverse square law in electrostatics. State the factors on which electrostatic force depends and express the law in vector form.
State Gauss's Theorem in electrostatics. Using Gauss's theorem, derive an expression for the electric field intensity at a point due to an infinitely long straight line charge having uniform linear charge density $\lambda$.
Two point charges $+2\ \mu\text{C}$ and $-2\ \mu\text{C}$ are placed $3\text{ cm}$ apart, forming an electric dipole. This dipole is placed in a uniform electric field of magnitude $2 \times 10^5\text{ N/C}$ making an angle of $30^\circ$ with the direction of the field. Calculate:
- The magnitude of the electric dipole moment.
- The torque acting on the electric dipole.
- The work done in rotating the dipole from stable equilibrium ($\theta = 0^\circ$) to unstable equilibrium ($\theta = 180^\circ$).
- The potential energy of the dipole at its present position ($\theta = 30^\circ$).
What is an electric dipole? Define electric dipole moment and state its SI unit and dimensional formula. Derive an expression for the electric field intensity at a point situated on the axial line (end-on position) of an electric dipole.
Question 1: (a) State Gauss's Law in electrostatics. (b) Using Gauss's law, derive an expression for the electric field intensity at a distance $r$ from an infinitely long straight thin wire carrying a uniform linear charge density $\lambda$. (c) Draw a neat graph showing the variation of electric field $E$ with distance $r$ from the wire.
Question 2: (a) Define an Electric Dipole and Electric Dipole Moment. Is dipole moment a scalar or vector quantity? State its SI unit. (b) Derive an expression for the electric field intensity at a point situated on the axial position (end-on position) of an electric dipole. (c) What happens when an electric dipole is placed in a uniform external electric field? Write the expression for the torque acting on it.
(a) State Gauss's Theorem in electrostatics. Using Gauss's law, derive an expression for the electric field intensity at a distance $r$ from an infinitely long straight uniformly charged thin wire with linear charge density $\lambda$.
(b) An infinitely long line charge produces an electric field of magnitude $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. Calculate the linear charge density.