University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2019
Views:

114

Pages:

17
Author:

Scalondrof11

**CH29: Magnetic Field Due to Currents** [Image of a current-carrying wire with a magnetic field line] dB = (μ₀/4π) * (i ds sinθ) / r² Biot-Savart Law μ₀ = 4π x 10^-7 (T.m/A) Permeability of the medium [μ₀] = [B][L]/[I][L] = T.m²/A.m = T.m/A dB = (μ₀/4π) * (i ds x r) / r² General formula = ds x r| = ds x r sinθ **Ex: Hollow wire** B = 2πrcb **1. Uniform dist:** ∫Bds cosθ = μ₀Ienc B(2πr) = μ₀ (r²-a²) **2. Non-uniform dist: J(r) = Cr²** i = ∫Jda = ∫J2πrdr ∫Bds cosθ = μ₀Ienc B(2πr) = μ₀ (πC/2)(r⁴ - a⁴) B = (μ₀C/4r)(r⁴ - a⁴) **Magnetic Field of a Solenoid** [Image of a solenoid with Amperian loop] * Amperian Loop: ∮B.ds = μ₀Ienc ∮Bds cosθ = μ₀Ienc Bh = μ₀Ienc Bh = μ₀ (Ni) Bh = μ₀ (nkI) B = μ₀ni * n = number of turns per unit length * n = N/l (N = total turns, l = length of the solenoid) **Magnetic Field of a Toroid** ∮Bds cosθ = μ₀Ienc B(2πr) = μ₀Ni B = (μ₀Ni) / (2πr) [Image of a toroid with magnetic field lines] **vs Solenoid** Bsolenoid = μ₀ni [Image of a solenoid] **vs Toroid** Btoroid = (μ₀Ni) / (2πr)