Amperes Law Magnetic Field Loop A closed loop

Ampere’s Law

Magnetic Field Loop ] A closed loop can be drawn in a magnetic field. B I • Any shape path • Include direction along path ] Ampere deduced a relationship between the loop and currents.

Current Through Loop ] The loop can be broken down into separate segments Dl. ] The field parallel to an individual segment is B║. • Opposite to loop direction is negative ] The net current is the sum of all currents into the loop. • Out of loop is negative

Ampere’s Law ] The sum of the parallel fields is based on the field direction on the perimeter of the loop. ] The sum of the currents is based on the area within the loop. ] Ampere’s law states that these sums are equal.

Application to Line B I ] Apply Ampere’s law to a straight line current in a wire. ] Use a loop that follows a circular field line. • B always parallel to Dl ] One current through the loop I. ] Ampere’s law gives the expected result.

Solenoid Current ] For a field inside the solenoid use four straight lines to make the loop. ] The loop length L along the NI L axis defines the number of turns of wire in the loop. l B

Solenoid Field ] For a field inside the solenoid use four straight lines to make the loop. NI B ] B is perpendicular to radial segments. • No contribution to sum l ] Outer segment has no field if solenoid is long enough. ] The only contribution is the inside segment.

Solenoid Match ] Ampere’s law can be applied to compare the current and the field. NI • Independent of choice of line inside the coil B l