Question

A long, thin solenoid has 870 turns per meter and radius 2.70 cm . The current in the solenoid is increasing at a uniform rate of 64.0 A/s

What is the magnitude of the induced electric field at a point 0.520 cm

from the axis of the solenoid? (in V/m)

What is the magnitude of the induced electric field at a point 1.30 cm

from the axis of the solenoid? (in V/m)

Answer 1

Induced emf inside solenoid is given by,

   .......................(1)

where is magnetic flux, B is magnetic flux density and A is area of crosssection of solenoid

Magnetic field B in solenoid is given by,

.......................(2)

where is permeability of free space, n is number of turns per unit length and

I is current passing through solenoid .

from eqn.(1) and eqn.(2), we get,

Electric field E is obtained from ,

Hence E = / ( 2r )

Electric field at r = 0.52 cm = 5.935 10^-5 / ( 2 0.52 10^-2 ) = 1.817 10^-3 V/m

Electric field at r = 1.3 cm = 5.935 10^-5 / ( 2 1.3 10^-2 ) = 7.266 10^-4 V/m