Along, thin solenoid has 390 turns per meter and a radius of 1.20 cm. the current in the solenoid is increasing at a uniform rate didt. the magnitude of the induced electric field at a point which is near the center of the solenoid and a distance of 3.48 cm from its axis is 8.00×10−6 v/m.
calculate di/dt.

To solve this problem it is necessary to apply the concepts related to Faraday's law and the induced emf.

By definition the induced electromotive force is defined as

Where,

Electric field

B = Magnetic Field

A = Area

At the theory the magnetic field is defined as,

Where,

N = Number of loops

I = current

Permeability constant

We know also that the cross sectional area, is the area from a circle, and the length is equal to the perimeter then

A = \pi r^2

l = 2\pi r

Replacing at the previous equation we have that

Where,

R = Radius of the solenoid

r = The distance from the axis

Re-arrange to find the current in function of time,

Replacing our values we have

5 w for 1hr = 5x60x60 joules=300x60=3000x6=18,000j as total energy conversion. efficiency of bulb needed for radiant to thermal within 18000