Magnetic Effect of Current Formula Sheet PDF
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This document is a formula sheet on magnetic effects of electric current. It includes formulas for Biot-Savart law, magnetic fields due to straight and circular current loops, Ampere's circuital law, magnetic forces, and more. It is suitable for secondary school physics students.
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# Magnetic Effect of Current ## Formula Sheet ### Biot-Savart Law: * dB = (µ₀ i dℓ sin θ) / (4πr²) * d **B** = (µ₀i d**ℓ x **r) / (4πr³) ### Magnetic Field Due to Straight Current Carrying Conductor: * B = (µ₀i/4π) (sinθ₁ + sinθ₂) * For infinite wire * B = (µ₀i / 2πa) * For semi-infinite w...
# Magnetic Effect of Current ## Formula Sheet ### Biot-Savart Law: * dB = (µ₀ i dℓ sin θ) / (4πr²) * d **B** = (µ₀i d**ℓ x **r) / (4πr³) ### Magnetic Field Due to Straight Current Carrying Conductor: * B = (µ₀i/4π) (sinθ₁ + sinθ₂) * For infinite wire * B = (µ₀i / 2πa) * For semi-infinite wire * B = (µ₀i / 4πa) ### Magnetic Field of a Circular Current Loop * At center of loop: B = (µ₀i / 2a) * At an axial point at distance r: * B = (µ₀ia² / 2(r² + a²)^(3/2) ### Ampere's Circuital Law * ∮ **B** . d**ℓ** = µ₀I ### Magnetic Field of a Straight Solenoid: * (i) B = µ₀ni (At a point well inside the solenoid) * (ii) B end = ±µ₀ni / 2 ### Magnetic Field of a Toroidal Solenoid: * B = µ₀ni / 2πr # Force on a Charge Moving in a Magnetic Field * F = qvBsinθ * F = q( **v x B** ) ### Lorentz Force: * F = q( **E** + **v x B** ) ### Motion of Charge Inside a Magnetic Field: * When **v**⊥**B** circular path. * r = mv / qB * ω = v / r = qB / m * T = 2πm / qB * v = 2πr / T = qB / 2πm * Pitch = 2πmu / (qB) ### Magnetic Force Due to Straight Current Carrying Conductor: * F = Biℓsinθ * F = i( **ℓ x B** ) ### Magnetic Force in Between Two Parallel Straight Current Carrying Conductors * F₁₂ = F₂₁ = (µ₀I₁I₂ℓ / 2πd) ### Cyclotron: * (KE) max = q²B²r² / 2m ### Torque on Current Carrying Coil In a Magnetic Field: * τ = BiNA sinθ * m = magnetic moment = NiA * τ = mB sinθ * τ = ( **m x B** ) # Galvanometer: * Deflection & Current in the coil: * θ = (BINA / K) ### Current Sensitivity of a Galvanometer: * Is = (θ / I) = (BNA / K) ### Voltage Sensitivity of a Galvanometer: * Vs = θ / V = (BNA / KR) ### Conversion of Galvanometer into Ammeter: * S = (Ig / (Ig + Sh)) * Rea = 1 / (1 / S + 1 / Sh) = (S Sh) / (S + Sh) * Req = (S Sh) / (S + Sh) ### Conversion of Galvanometer into Voltmeter: * V = Ig(G + R) * R = V / Ig - G * Rea = R + G
