29 example 8 303l magnetic force and field ch29 3

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Unformatted text preview: B = BA cos θ ΦB = 0 Φ B = BA • The net magnetic flux through any closed surface is always zero 303L: Magnetic Force and Field (Ch.29) Example 8 303L: Magnetic Force and Field (Ch.29) 3 Displacement Current SUMMARY General form of Ampere’s law Magnetic Force and Field rr dq ∫ B ⋅ ds = µ0 I = µ0 dt • Magnetic force: • Ampere’s law in this form is valid only if any electric fields present are constant in time • Displacement current dΦ E Id = ε 0 dt • General form of Ampere’s law: rr dΦ E ∫ B ⋅ ds = µ0 (I + I d ) = µ0 I + µ0ε 0 dt • The SI unit of B is the tesla (T) ε0 ⇒ dΦ E dq Id = ε 0 = dt dt r r µ Ids × r ˆ dB = 0 4π r 2 • The magnetic force per unit length between two parallel wires separated by a distance a and carrying currents I1 and I2: • Ampere’s law: • Magnetic flux: rr q Φ E = ∫ E ⋅ dA = EA = rr ∫ B ⋅ ds = µ 0 I 303L: Magnetic Force and Field (Ch.29) r µII F1 / l = 0 1 2 2πa rr Φ B = ∫ B ⋅ dA • Gauss’s law of magnetism the net magnetic flux through any closed surface is zero • Ampere-Maxwell law: • Magnetic fields are produced both by currents and time-varying electric fields r rr FB = I L'× B • Force on a current-carrying conductor: • Biot-Savart law: r rr FB = q v × B r r ∫ B ⋅ ds = µ (I + I ) = µ I + µ ε 0 d 0 00 dΦ E dt 303L: Magnetic Force and Field (Ch.29) 4...
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