Shortcut Methods

JEE NUMERICALS


  1. Hollow Conducting Sphere Electric Field:

(i) Inside the sphere (r < R) E=0

(ii) Outside the sphere (r > R) E=14πϵ0Qr2

  1. Solid Conducting Sphere Electric Field:

(i) Inside the sphere (r < R) E=14πϵ0QrR3

(ii) Outside the sphere (r > R) E=14πϵ0Qr2

  1. Concentric Conducting Spheres Electric Field:

(i) Inside the inner sphere (r < R1) E=0

(ii) Between the spheres (R1 < r < R2) E=14πϵ0Q1r2

(iii) Outside the outer sphere (r > R2) E=14πϵ0Q1+Q2r2

  1. Cylindrical Capacitor Electric Field:

(i) Inside the inner cylinder (r < R1) E=0

(ii) Between the cylinders (R1 < r < R2) E=12πϵ0Q1r

  1. Parallel-Plate Capacitor Electric Field: E=σϵ0=QAdϵ0

CBSE BOARD NUMERICALS


  1. Conducting Sphere (CBSE Board) Electric Field:

E=14πϵ0Qr2 for r>R

  1. Two Point Charges Electric Field: E=14πϵ0[Q1(rs)2+Q2s2]

  2. Dipole Electric Field: E=14πϵ02Qdr3

  3. Uniform Electric Field Electric Field: $$\vec{E}=\vec{E}Q+\vec{E}{uniform}=\dfrac{1}{4\pi \epsilon_0}\dfrac{Q}{r^2}\hat{r}+E\hat{i}$$

  4. Current-Carrying Wire Magnetic Force: F=ILBsinθn^