- Gauss’s law is useful for finding the electric field in highly symmetric charge distributions (line, plane, sphere).
- For an infinitely long charged wire, the electric field is radial and depends only on the distance r from the wire.
- Electric field due to an infinite line charge decreases with distance:
E = \[\frac{\lambda}{2\pi\varepsilon_0r}\] - For an infinite plane sheet, the electric field is uniform and does not change with distance.
- Electric field due to an infinite plane sheet is:
E = \[\frac{\sigma}{2\varepsilon_0}\] - For a uniformly charged spherical shell, the field outside behaves like a point charge at the centre:
E = \[\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}\] - Inside a uniformly charged spherical shell, the electric field is zero.
Definitions [2]
Definition: Dielectric Constant
The ratio of the permittivity of a medium to the permittivity of vacuum.
K = ε / ε₀
OR
Dielectric constant is the factor by which the capacitance of a capacitor increases when a dielectric is completely inserted between its plates.
Definition: Permittivity of a Medium
The product of vacuum permittivity and dielectric constant of the medium.
ε = ε₀K
Theorems and Laws [1]
State Gauss’ Law.
The electric flux (ΦE) through any closed surface is equal to `1/in_0` times the ‘net’ change q enclosed by the surface.
ΦE = `oint vec E d vec A`
= `q/in_0`
∈0 = Permittivity of free space.
Gauss’ theorem states that the net electric flux over a closed surface is `1/epsilon_0` times the net electric charge enclosed by the surface.
Φ = `oint vec E * d vec A`
= `q/epsilon_0`
Key Points
Key Points: Applications of Gauss' Theorem
Important Questions [15]
- Electric Intensity Outside a Charged Cylinder Having the Charge per Unit Length 'λ' at a Distance from Its Axis is
- A 36 cm long sonometer wire vibrates with frequency of 280 Hz in fundamental mode, when it is under tension of 24.5 N. Calculate linear density of the material of wire.
- The Electric Field Intensity Outside the Charged Conducting Sphere of Radius ‘R’, Placed in a Medium of Permittivity ∈ at a Distance ‘R’ from the Centre of the Sphere in Terms of Surface Charge Densit
- Find the Mechanical Force per Unit Area of the Charged Conductor.
- The Energy Density at a Point in a Medium of Dielectric Constant 6 is 26.55 × 106 J/M3. Calculate Electric Field Intensity at that Point
- Electric Intensity Due to a Charged Sphere at a Point Outside the Sphere Decreases with ?
- A Parallel Plate Air Condenser Has a Capacity of 20µF. What Will Be a New Capacity If: 1) The Distance Between the Two Plates is Doubled? 2) A Marble Slab of Dielectric
- Draw a Neat Labelled Diagram of a Parallel Plate Capacitor Completely Filled with Dielectric.
- Define Capacitance of a Capacitor and Its Si Unit.
- Obtain an Expression for Electric Field Intensity at a Point Outside Uniformly Charged Thin Plane Sheet
- A Cube of Marble Having Each Side 1 Cm is Kept in an Electric Field of Intensity 300 V/M. Determine the Energy Contained in the Cube of Dielectric Constant 8.
- Intensity of Electric Field at a Point Close to and Outside a Charged Conducting Cylinder is Proportional To
- What is the Charge on the Capacitor?
- A network of four capacitors of 6 μF each is connected to a 240 V supply. Determine the charge on each capacitor.
- With the Help of a Neat Diagram, Describe the Construction and Working of Van De Graff Generator.
Concepts [11]
- Applications of Gauss' Theorem
- Mechanical Force on Unit Area of a Charged Conductor
- Energy Density of a Medium
- Dielectrics
- Concept of Condenser
- The Parallel Plate Capacitor
- Capacity of Parallel Plate Condenser
- Effect of Dielectric on Capacity
- Energy of Charged Condenser
- Condensers in Series and Parallel,
- Van-deGraaff Generator
