Magnetic Field and Electric field outside a long solenoid

darkar

Hello,

The question goes like this:

A long solenoid has n turns per unit length and carries a current given by I=I₀sinωt. The solenoid has a circular cross section of radius R. Find the induced electric field at a radios r from the axis of the solenoid for (a) r<R (b) r>R

Well, i got the first part as E=μR²N²ωI₀cos(ωt)/(2Rl). Does this looks like it?

For the second bit, i found it as zero. But i am not really sure. And if it is zero, What should i say?

anaemic1

Hello there,

You'll have to excuse me because I'm not using the greek symbols.

(a) r<R,

int(E.dl)=-d(B.Area)/dt (definition of induced emf) take loop around

E.2*pi*r = -pi*(r^2)*mu*n*I*omega*cos(omega*t)

E= -(mu*n*I*omega*r*cos(omega*t))/2

is the induced field inside solenoid. Your answer is close but use r instead of R (since we are inside).

(b) r>R, outside

You are confusing with the case when magnetic field is zero outside long solenoid due to cancellations between field due to currents in successive & opposite loops.

In this case, (r>R...remember loop is longer)

E*2*pi*r = -pi*(R^2)*mu*n*I*omega*cos(omega*t)

(remember flux is over an area defined by pi*(R^2))

E = -(mu*n*I*omega*(R^2)*cos(omega*t))/ (2*r)

is the induced electric field outside.


Hope that helps,
Rama

berkeman

Are you sure they are asking about Electric fields? That doesn't make much sense. More often, you will be asked to solve for the magnetic field as a function of radius for the solenoid....

darkar

Yea, i m asked to find electric field. And i just found out this is one of the question found from the textbook. And yes, thats the correct answers! but i am still not sure why it is not zero. isnt that when theres no magnetic field, theres no electric field as well?

Physics Monkey

darkar,

To understand why there is an electric field outside the solenoid, just think about Faraday's Law. If you draw a loop around the solenoid, the magnetic flux through the loop is changing as a function of time, right? Even though there is no magnetic field outside the solenoid there is still a changing magnetic flux (from the field inside the solenoid). What does this tell you about the electric field?

darkar

Yea, thats amaze me. Why can there be magnetic flux but no magnetic field. So lif theres magnetic field, the magnetic flux is constant?