Govt. Exams
For undeflected motion, electric and magnetic forces must balance: qE = qvB, giving E = vB. This is the principle of velocity selector used in mass spectrometers.
For equal perimeter, circle encloses maximum area (isoperimetric inequality). Since magnetic moment m = IA, circular loop with larger area has larger magnetic moment.
For balanced bridge: P/Q = R/S. Check: 10/15 = 20/30 → 2/3 = 2/3. The bridge is balanced, so no current flows through galvanometer (zero reading).
BCS theory explains superconductivity: below critical temperature, electrons form Cooper pairs with no scattering, resulting in zero resistance.
For infinite ladder: Rₑq = 1 + (Rₑq×1)/(Rₑq+1). Solving: Rₑq² - Rₑq - 1 = 0, giving Rₑq = (1+√5)/2 ≈ 1.618Ω (Golden ratio)
R = ρL/A. If L increases by 10% and volume constant, A decreases by ~9.1%. New R = 1.1R₀/0.91 ≈ 1.21R₀, so 21% increase.
With R = 0, by I = V/R, current becomes infinite. In practice, voltage source cannot be maintained across a superconductor
By Ohm's law in microscopic form: E = ρJ. Inside the conductor, electric field maintains the drift of electrons
Maximum power transfer theorem: Load resistance equals internal resistance. R = r = 2Ω for maximum power
In semiconductors, increased temperature promotes more electrons from valence to conduction band, increasing carrier concentration and decreasing resistance
