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Ampere’s Law

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**Magnetic Field Loop A closed loop can be drawn in a magnetic field.**

Any shape path Include direction along path Ampere deduced a relationship between the loop and currents. B I

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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

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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.

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Application to Line 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. B I

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

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

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

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