Electrostatics: Charges & Fields (JEE Advanced
Level Notes)
1. Fundamentals
Charge is quantized: q = ne
Coulomb Law: F = (1/4πε■)(q■q■/r²)
Electric Field: E = (1/4πε■)(q/r²)
Superposition principle (vector sum)
2. Electric Field Distributions
Ring (axis)
E = (1/4πε■)(qx/(x²+R²)^(3/2))
Max at x = R/√2
Disk (axis)
E = (σ/2ε■)(1 - x/√(x²+R²))
Limit → infinite sheet: E = σ/2ε■
Sphere
Conducting: Inside E=0, outside like point charge
Non-conducting: Inside E ∝ r, Outside ∝ 1/r²
3. Potential
Point: V = (1/4πε■)(q/r)
Ring: V = (1/4πε■)(q/√(x²+R²))
Disk: V = (σ/2ε■)(√(x²+R²) - x)
Solid sphere: V_inside = (1/4πε■)(Q/2R³)(3R² - r²)
Relation: E = -dV/dr
4. Key Derivations (Conceptual)
Ring: symmetry → only axial components survive
Level Notes)
1. Fundamentals
Charge is quantized: q = ne
Coulomb Law: F = (1/4πε■)(q■q■/r²)
Electric Field: E = (1/4πε■)(q/r²)
Superposition principle (vector sum)
2. Electric Field Distributions
Ring (axis)
E = (1/4πε■)(qx/(x²+R²)^(3/2))
Max at x = R/√2
Disk (axis)
E = (σ/2ε■)(1 - x/√(x²+R²))
Limit → infinite sheet: E = σ/2ε■
Sphere
Conducting: Inside E=0, outside like point charge
Non-conducting: Inside E ∝ r, Outside ∝ 1/r²
3. Potential
Point: V = (1/4πε■)(q/r)
Ring: V = (1/4πε■)(q/√(x²+R²))
Disk: V = (σ/2ε■)(√(x²+R²) - x)
Solid sphere: V_inside = (1/4πε■)(Q/2R³)(3R² - r²)
Relation: E = -dV/dr
4. Key Derivations (Conceptual)
Ring: symmetry → only axial components survive
