Electric Charge and Coulomb's Law

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Questions and Answers

What does the symbol $ ho$ represent in the equation $dq = ho dV$?

Electric potential

Volume charge density (correct)

Electric field intensity

Net force on charge

The electric field intensity is a scalar quantity.

False

What is the SI unit of electric field intensity?

N/C

If $q > 0$, the electric field direction is _____ the source charge.

away from Signup and view all the answers

Match the following concepts with their definitions:

dq = Differential charge element E = Electric field intensity F = Net force on charge r = Distance from charge to point of interest Signup and view all the answers

In which orientation is an electric dipole in stable equilibrium?

Parallel to the electric field Signup and view all the answers

The net electric flux emerging from a closed surface enclosing a net charge is zero when the algebraic sum of charges is zero.

True Signup and view all the answers

What is the formula for the electric field due to a thin, infinitely long straight wire of uniform linear charge density λ at a distance r?

E = λ / (2πε₀r) Signup and view all the answers

For a uniformly charged thin spherical shell at a point outside the shell (r > R), the electric field is given by E = __________.

1/(4πε₀) * (q/r²) Signup and view all the answers

Match the following Gaussian surfaces with their corresponding shapes:

Sphere = Concentric sphere Cylinder = Coaxial cylinder Plate = Cube or cuboid Infinite rod = Coaxial cylinder Signup and view all the answers

What does Millikan's oil drop experiment demonstrate?

Charge cannot be a fractional multiple of the elementary charge. Signup and view all the answers

The net charge in an isolated system can change over time.

False Signup and view all the answers

What is the formula for Coulomb's law?

F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2} Signup and view all the answers

The total charge of a system is the _________ sum of its individual charges.

algebraic Signup and view all the answers

Which of the following statements is true about electric field intensity?

Its SI unit is N/C or V/m. Signup and view all the answers

Match the types of charge distribution with their definitions:

Linear Charge Distribution = Distribution along a line Surface Charge Distribution = Distribution over a surface Volume Charge Distribution = Distribution within a volume Electric Field Intensity = Force per unit positive charge at a point Signup and view all the answers

Electric charge is invariant and depends on the motion of the observer.

False Signup and view all the answers

In continuous charge distribution, $dq$ for a surface is defined as $dq = _______ dS$.

σ Signup and view all the answers

Study Notes

Millikan's Oil Drop Experiment

Demonstrated the quantized nature of electric charge.
Established that charge exists in whole multiples of elementary charge (e), prohibiting fractional charges.

Conservation of Charge

The total charge in an isolated system is constant over time.
Charge can only be transferred, not created or destroyed.

Electric Charge Properties

Electric charge is additive, determined by the algebraic sum of individual charges.
Charge remains invariant, independent of motion or observation.

Coulomb's Law

Describes the electrostatic force between two point charges: $$F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}$$
$F$ is the force between charges $q_1$ and $q_2$, separated by distance r.
$\epsilon_0$ (permittivity of free space) is approximately $8.85 \times 10^{-12} \text{ C}^2/\text{N m}^2$ or $9 \times 10^{9} \text{ Nm}^2/\text{C}^2$ in inverse form.
In a medium, $\epsilon_0$ changes to $\epsilon_0 \epsilon_r$ (dielectric constant).

Continuous Charge Distribution Types

Charge can distribute continuously in three ways:
- Linear Charge Distribution
- Surface Charge Distribution
- Volume Charge Distribution

Linear Charge Distribution

Linearly distributed charge expressed as: $$dq = \lambda dl$$
Forces calculated via: $$dF = \frac{1}{4\pi\epsilon_0} \frac{q_0\lambda dl}{r^2}$$
Net force on charge $q_0$: $$F = \frac{q_0\lambda}{4\pi\epsilon_0} \int \frac{dl}{r^2}$$

Surface Charge Distribution

Surface charge density expressed as: $$dq = \sigma dS$$
Total force on charge $q_0$: $$F = \frac{q_0}{4\pi\epsilon_0} \int \frac{\sigma dS}{r^2}$$

Volume Charge Distribution

Volume charge density represented as: $$dq = \rho dV$$

Electric Field Intensity

Defined as electric force per unit positive charge: $$E = \lim_{q_0 \to 0} \frac{F}{q_0}$$
SI units are N/C or V/m; it's a vector quantity.

Electric Field Intensity Due to a Point Charge

Given by: $$E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$$
For a positive charge, field lines point radially outward; for a negative charge, they point inward.

Electric Dipole in Uniform Electric Field

Dipole orientation impacts stability; parallel alignment is stable, while antiparallel is unstable.

Gauss's Law

Relates electric flux through a closed surface to the enclosed charge: $$\oint \vec{E} \cdot \vec{dA} = \frac{q}{\epsilon_{0}}$$
Specific Gaussian surface shapes depend on charge configurations (spherical, cylindrical, etc.).

Electric Field Due to Specific Charge Distributions

Thin, infinitely long straight wire: $$E = \frac{\lambda}{2\pi\epsilon_{0}r}$$
Uniformly charged thin spherical shell:
- Outside shell ($r>R$): $$E = \frac{1}{4\pi\epsilon_0}\frac{q}{r^{2}}$$
- On the shell ($r=R$): $$E = \frac{1}{4\pi\epsilon_0}\frac{q}{R^{2}}$$
- Inside shell ($r<R$): Field intensity is zero.

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Description

This quiz covers key concepts in electrostatics, including Millikan's oil drop experiment, the conservation of charge, and the properties of electric charge. It also explains Coulomb's Law and how it quantifies the electrostatic force between point charges. Test your understanding of these fundamental principles of physics.