Electric current The Ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce a force between them equal to 2 × 10 -7 Newton per meter of length.
Fig P30-20, p.940 Magnetic Flux B = BdA = BAcos
Ampère’s Law One More Time Ampere’s law states that the line integral of B. ds around any closed loop equals o I where I is the total steady current passing through any surface bounded by the closed loop.
Apply Ampere’s Law to red loop for a wire with a constant current I Now introduce a capacitor to interrupt the the circuit. What’s wrong? Use a power supply that will keep current constant as the cap is charged: +Q/-Q on left/right plate. Now Apply Ampere’s Law again.
Now introduce a capacitor to interrupt the the circuit. If our power supply is strong enough to keep I constant, the gray surface will give B = 0! What’s wrong? Assume that I is constant. Apply Ampère’s Law to either the, white or gray surfaces, both of which are bounded by the red loop. This leads to:
If the power supply can keep the current constant, the cap. will be charged: +Q/-Q on left/right plate. This establishes an E-field between the two plates. E = EdA = Q/ o Electric flux will change in time corresponding to an effective current called the Displacement Current