Important Electrostatics Formulas For JEE
Electrostatics is a fundamental branch of physics that deals with the study of electric charges at rest. It plays a crucial role in various engineering and science fields, and a strong understanding of electrostatics is essential for JEE (Joint Entrance Examination) aspirants. In this article, we will explore some of the most important electrostatics formulas that you should be familiar with to excel in your JEE preparations.
1. Coulomb's Law
Coulomb's Law describes the electrostatic force between two point charges. It is one of the foundational principles of electrostatics and is mathematically expressed as:
F = k * (|q1 * q2|) / r^2
Where:
- F is the magnitude of the electrostatic force.
- k is the electrostatic constant, approximately equal to 8.99 x 10^9 Nm^2/C^2.
- q1 and q2 are the magnitudes of the two point charges.
- r is the separation distance between the two charges.
2. Electric Field (E)
The electric field at a point in space is the force experienced by a unit positive test charge placed at that point. Mathematically, it is given by:
E = F / q
Where:
- E is the electric field.
- F is the force acting on the test charge.
- q is the magnitude of the test charge.
3. Electric Potential (V)
The electric potential at a point is the work done in bringing a unit positive charge from infinity to that point. The formula for electric potential is:
V = k * (q / r)
Where:
- V is the electric potential.
- k is the electrostatic constant.
- q is the magnitude of the point charge creating the potential.
- r is the distance from the point charge to the point where potential is calculated.
4. Electric Potential Energy (U)
The electric potential energy of a system of point charges is the work done in assembling those charges from infinity. It is calculated using the formula:
U = k * (|q1 * q2|) / r
Where:
- U is the electric potential energy.
- k is the electrostatic constant.
- q1 and q2 are the magnitudes of the two point charges.
- r is the separation distance between the two charges.
5. Gauss's Law
Gauss's Law relates the electric flux through a closed surface to the total charge contained within that surface. Mathematically, it is expressed as:
Φ = E * A = (q_enclosed) / ε₀
Where:
- Φ is the electric flux through a closed surface.
- E is the electric field.
- A is the area of the closed surface.
- q_enclosed is the total charge enclosed by the surface.
- ε₀ is the permittivity of free space, approximately equal to 8.85 x 10^(-12) C^2/Nm^2.
6. Capacitance (C)
Capacitance measures the ability of a conductor to store electrical charge. It is given by the formula:
C = Q / V
Where:
- C is the capacitance.
- Q is the charge stored on the conductor.
- V is the potential difference across the conductor.
7. Ohm's Law (for capacitors)
Ohm's Law for capacitors relates the current (I), voltage (V), and capacitance (C) in a charging or discharging capacitor:
I = C * dV/dt
Where:
- I is the current.
- C is the capacitance.
- dV/dt is the rate of change of voltage with respect to time.
8. Energy Stored in a Capacitor (U)
The energy stored in a charged capacitor is given by:
U = (1/2) * C * V^2
Where:
- U is the energy stored.
- C is the capacitance.
- V is the voltage across the capacitor.
9. Torque on a dipole placed in the electric field
10. Potential energy of a dipole
These are some of the fundamental electrostatics formulas that are crucial for your JEE preparations. Understanding these formulas and their applications will help you solve a wide range of electrostatics problems that may appear on the exam. Make sure to practice these concepts and apply them to various problems to build your proficiency in electrostatics.
Important Electrostatics Formulas For JEE FAQs
Q1. What is the formula for Coulomb's law?
Ans.
- Formula: F = k * (|q1 * q2|) / r^2
- Explanation: This formula describes the electrostatic force (F) between two point charges (q1 and q2) separated by a distance (r), where k is the Coulomb's constant.
Q2. What is the formula for the electric field due to a point charge?
Ans.
- Formula: E = k * (|q|) / r^2
- Explanation: This formula calculates the electric field (E) at a point in space Because of a point charge (q) situated at a distance (r) from that point.
Q3. What is the formula for the electric field due to a continuous charge distribution?
Ans.
- Formula: E = (1 / 4πε₀) * ∫(dq) / r^2
- Explanation: This formula calculates the electric field (E) at a point in space due to a continuous charge distribution, represented by the integral of infinitesimal charge elements (dq) over the distribution.
Q4. What is the formula for electric potential (voltage)?
Ans.
- Formula: V = k * (|q|) / r
- Explanation: This formula calculates the electric potential (V) at a point in space Because of a point charge (q) situated at a distance (r) from that point.
Q5. What is the formula for the electric potential energy of a system of point charges?
Ans.
- Formula: U = k * (|q1 * q2|) / r
- Explanation: This formula calculates the electric potential energy (U) of a system of two point charges (q1 and q2) separated by a distance (r).
