Numerical Range Shortcuts

Numerical Range 1: Magnetic Force

• For magnetic force calculations involving a straight wire, remember the formula F = BIL, where F is in Newtons, B is in Teslas, I is in Amperes, and L is in meters.
• For practical purposes, assume B ≈ 0.5 T and L ≈ 0.1 m for rough estimations.
• If the current I is given in milliamperes (mA), convert it to Amperes by dividing by 1000 (I in A = I in mA / 1000).

Numerical Range 2: Torque on a Current Loop

• For torque calculations involving a current loop, use the formula τ = NIAB sinθ, where τ is in Newton-meters, N is the number of turns, I is in Amperes, A is the loop’s area in square meters, B is in Teslas, and θ is the angle between the loop and the magnetic field in degrees.
• Remember that sinθ = 0 for θ = 0° and sinθ = 1 for θ = 90°.

Numerical Range 3: Magnetic Field of a Current-Carrying Wire

• For magnetic field calculations near a long straight wire, use the formula B = μ₀I/(2πr), where B is in Teslas, μ₀ is the permeability of free space (4π × 10^(-7) N/A^2), I is in Amperes, and r is the distance from the wire in meters.
• When r is given in centimeters, convert it to meters by dividing by 100 (r in m = r in cm / 100).

Numerical Range 4: Magnetic Field of a Solenoid

• For solenoids, use the formula B = μ₀nI, where B is in Teslas, μ₀ is the permeability of free space (4π × 10^(-7) N/A^2), n is the number of turns per unit length in turns per meter, and I is the current in Amperes.
• When n is given in turns per centimeter, convert it to turns per meter by multiplying by 100 (n in turns/m = n in turns/cm * 100).