Shortcut Methods
JEE MAIN & ADVANCED Numerical Shortcuts:
Numerical 1:
- Potential at P due to 1st charge (V₁) = k(10⁻⁹ / 0.2) = 9 X 10⁹ V
- Potential at P due to 2nd charge (V₂) = k(-2 X 10⁻⁹ / 0.15) = -12 X 10⁹ V
- Net potential at P (V) = V₁ + V₂ = -3 X 10⁹ V
Numerical 2:
- Potential at point due to +1 µC charge (V₁) = k(+10⁻⁶ / 0.3) = 3 X 10³ V
- Potential at point due to -2 µC charge (V₂) = k(-2 X 10⁻⁶ / 0.2) = -9 X 10³ V
- Net potential at point (V) = V₁ + V₂ = -6 X 10³ V
Numerical 3:
- Work done (W) = qV = (5 X 10⁻⁹ C) (100 V) = 5 X 10⁻⁷ J
Numerical 4:
- Potential energy (U) = k(q₁ q₂) / r = (9 X 10⁹ N m²/C²) (2 X 10⁻⁶ C)² / 0.5 m = 72 X 10⁻³ J
Numerical 5:
- Charge stored (Q) = CV = (2 X 10⁻⁶ F) (100 V) = 2 X 10⁻⁴ C
CBSE BOARD Numerical Shortcuts:
Numerical 1:
- Electric potential on the surface (V) = kq / r = (9 X 10⁹ N m²/C²) (10 X 10⁻⁹ C) / (0.1 m) = 90 V
Numerical 2:
- Charge stored (Q) = CV = (20 X 10⁻⁶ F) (9 V) = 180 X 10⁻⁶ C
Numerical 3:
- Potential difference (V) = Ed = (100 N/C) (5 X 10⁻² m) = 5 V
Numerical 4:
- Capacitance (C) = ε₀(A / d) = (8.85 X 10⁻¹² C²/N m²) (100 X 10⁻⁴ m²) / (2 X 10⁻³ m) = 0.44 pF
Numerical 5:
- Magnitude of electric field (E) = F / q = (5 X 10⁻¹² N) / (1.6 X 10⁻¹⁹ C) = 3.125 X 10⁷ N/C
