Question

A long, thin solenoid has 600 turns per meter and radius 2.6 cm. The
current in the solenoid is increasing at a uniform rate dI/dt. The induced
electric eld at a point near the center of the solenoid and 3.80 cm from
its axis is 8.00 10 -5 V/m. Calculate dI/dt

Answer 1

SOLUTIONS

According to the Faraday's Law:

Where;

is the induced electric field

is the diferential length

is the magnetic flux

is the time

Now, the magnetic flux can be written as;

For the area and the magnetic field. For a thin solenoid the magnetic field is:

Where:

is the number of turns for unit length

is the magnetic permeabiblity on free space

is the currrent

Similarly, the area of cross section of solenoid is:

With, the radius. Inserting (4), (3) into equation (2) we get:

Now, the current increases with time; therefore replacing (5) into equation (1) we have:

or

but:

Where,

is the distance from the axis.

Replacing (8) into (7) we get:

Isolating from equation (9) we get:

Replacing values:

solving we obtain: