ELECTROSTATICS

GAUSS’S THEOREM

INTRODUCTION

The fundamental field of physics known as ‘Electrostatics’ clearly explains the behaviour of electric charges at rest. Our understanding of electricity, magnetism, and light is built on electrostatics.Students in class 12 dig into the interesting principles of electric charges, Coulomb’s law, electric fields, electric potential, dielectrics, and capacitance in this study.

Electrostatics is a broad and significant subject with several applications in science and technology.Electrostatics, for example, is employed in the design of electrical devices that generate electricity and medical equipment. It’s also used to create new materials and technologies like solar cells and nanotechnology.

GAUSS’S THEOREM

Gauss’s theorem gives the relation between total flux passing through any closed surface and the net charge enclosed by that surface.

STATEMENT OF THE THEOREM

ELECTRIC FIELD DUE TO INFINITE LINE CHARGE – IMAGE

ELECTRIC FIELD DUE TO INFINITE LINE CHARGE

Impact-Site-Verification: d4730df8-152b-4957-aadb-30412856577c

ELECTRIC FIELD DUE TO A SPHERICAL SHELL

ELECTRIC FIELD DUE TO A SPHERICAL SHELL – INSIDE THE SPHERE

ELECTRIC FIELD DUE TO A SPHERICAL SHELL – OUTSIDE THE SPHERE

ELECTRIC FIELD DUE TO INFINITE PLANE SHEET

POTENTIAL ENERGY OF A DIPOLE

CAPACITOR AND ITS WORKING

INTRODUCTION

Using an electric field to store electrical energy, capacitors are passive electrical parts.Electrons gather in one plate and exit through the other when a voltage is applied across the plates, creating an electric field between them in the process. This results in the storage of electrical energy in the form of electric charge.A capacitor’s capacitance is influenced by the distance between its plates, their surface area, and the medium’s permittivity.

PARALLEL PLATE CAPACITOR – IMAGE

CAPACITOR

It is a two terminal electronic passive component(doesn’t produce energy) which is fit for putting away electric energy at the point when a voltage is applied across its plates.

• Electrons from the negative side of the battery will stream to the right plate and give its negative charges.The negative charges building up on right plate will repulse(repel) the negative charges on the left plate.
• Those negative charges will go towards the positive charge of the battery leaving behind positive charges on the left plate. Here is the reallocation of charges occurring.
• No current streams across the gap.The capacitor is supposed to be charged.

CAPACITANCE

Capacitance estimates how much charge put away per volt

CAPACITANCE OF A CAPACITOR

• Capacitance of a capacitor increments with decline in the detachment (decrease in separation) between the plates. As C ↑ when d ↓ C∝1/d
• Capacitance of a capacitor increments with space of cross-over of the plates C∝A
• Capacitance of the capacitor likewise relies upon the permittivity of the medium between the plates C ∝ɛ

CONCLUSION

In contemporary electronics and electrical engineering, capacitors are crucial components. They can carry out a variety of tasks, including filtering out undesirable signals and regulating voltage, thanks to their capacity to store energy.

These capacitors are used in many different applications, including lighting systems and audio systems (to provide a smooth and stable power supply and to filter out undesired frequencies and improve sound quality).communication systems (used in amplifiers, oscillators, and filters), medical (to store electrical energy and swiftly discharge it for medicinal uses), and automotive (to stabilise voltage).Anyone working in these fields needs to understand how capacitors work as well as their capacitance, and the formula for calculating capacitance is a helpful tool.

ENERGY STORED IN A CAPACITOR

CAPACITOR

A capacitor is a device for putting away electrical energy comprising of two conductors in neighboring and protected (insulated) from one another.

NO WORK DONE SINCE NO ELECTRIC FIELD

At first when the capacitor is being charged, no charge on one or the other plate . For this situation, the electric field between the plate is zero.

Let little small charge dq is moved from one plate (right) to another(left) plate. No work is needed since there is no electric field against it.

WORK DONE AGAINST THE ELECTRIC FIELD

Later next gradual charge  dq is to be moved from the right plate to left.Work must be done against the electric field.Energy is added each time at whatever point each steady charge dq is moved from right plate to passed on plate.

ENERGY OF CHARGED CAPACITOR MAY BE SAID TO RESIDE IN THE ELECTRIC FIELD BETWEEN THE PLATES.

MORE the VOLTAGE, THE MORE POTENTIAL DIFFERENCE AND HAVE GREATER ELECTRIC FIELD.

ENERGY STORED IN A CAPACITOR

POTENTIAL DIFFERENCE

WORK DONE IS STORED AS ELECTRICAL POTENTIAL ENERGY

ENERGY STORED IN A CAPACITOR – ALTERNATIVE METHOD

CAPACITANCE OF A CAPACITOR WITH DIELECTRIC

DIELECTRIC PLACED BETWEEN THE PLATES OF A CAPACITOR-IMAGE

d – Separation between the plates
t – Thickness of the dielectric slab
E_free – Uniform electric field( between the plates)
E_ind – Electric Field due to polarisation (inside the dielectric)
E_net – Net electric field(inside the dielectric)
C₀ – Capacitance with vacuum between plates
C – Capacitance with dielectric between plates
σ – Charge per area
σ_ind – Actuated (induced) charge per area

DIELECTRICS

• Dielectric forestalls(prevents) the two plates contacting each other.(keeps them separated)
• Dielectric builds the capacitance of the capacitor
• Dielectric builds the maximum potential difference between the plates before the capacitor begins to lead(conduct).

CAPACITANCE OF THE CAPACITOR (Vacuum between the plates)

• d – separation between the plates
• A – Area of the plate
• Ɛ₀ -Permittivity of free space
• Permittivity is the resistance to an electric field.
• Dielectrics truly do have higher permittivity (offer high resistance to the field)

FREE ELECTRIC FIELD (BETWEEN THE PLATES)

INDUCED ELECTRIC FIELD

NET ELECTRIC FIELD

DIELECTRIC CONSTANT

ELECTRIC FIELD

POTENTIAL DIFFERENCE BETWEEN THE PLATES

CAPACITANCE WITH DIELECTRIC