A solenoid with 1000 turns per meter and radius 2 cm carries an oscillating curr

Question

A solenoid with 1000 turns per meter and radius 2 cm carries an oscillating current I=5sin100pi*t, where I is in A and t is in s. What is the electric field induced at a radius r=5cm from the axis of the solenoid and the direction of the electric field when the I is increasing counterclockwise in the solenoid? A solenoid with 1000 turns per meter and radius 2 cm carries an oscillating current I=5sin100pi*t, where I is in A and t is in s. What is the electric field induced at a radius r=5cm from the axis of the solenoid and the direction of the electric field when the I is increasing counterclockwise in the solenoid?

Explanation / Answer

Let the number of turns per meter is n = 1000

Let the radius of the solenoid is R = 2 cm

Let the radius where electric field is calculated is r = 5 cm

Let the oscillating current is I = 5 * sin ( 100 * * t )

Current i = 5 A

Angular frequency = 100 / s

a)Now the induced electric field is given by

            E = { µ0 * n * i * * r cos( t ) } / 2 ………… ( 1 )

               = 4 * 10-7 * 1000 * 5 * 100 * 5 * cos( 100 t ) / 2

              = 2 * 25000 * 100 * 10-7 * 3.14 * 3.14 * cos( 100 t )

              = 4.9298 * cos ( 100 t ) V / m

b)The induced EMF is in a direction that opposes the change in B , so the direction of current is in clockwise direction

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