Recent content by oneofmany850

okay, I think I have finally wrapped my head around it now haha. Thanks for all your help. I see that it is because this magnetic field is time dependent which means that the curl of E is not zero which means that we can't write the E field as a gradient since the curl of a gradient is zero...

oh I see lol I forgot to do the integral. So yes your answer is correct. But why does the divergence of this equal zero and how do we know the curl of E is zero also?

the line integral of E equals the negative derivative of the surface integral of B. So $$E_\phi 2\pi r = -\frac{d}{dt}[Kr^n t \pi r^2] = -K\pi r^{n+2}$$ so $$E_\phi = -\frac{1}{2}K r^{n+1}$$ since we took the 2pi r over. Yes the phi component of the divergence was meant to be as you typed. But...

I think I'm dong the divergence in cylindrical coordinates incorrectly. I assumed because the E field is given for just the unit vector e_\phi then E_r and E_z equal zero. So just doing the partial differentiation on the phi component of E gives zero as there is no phi to differentiate?? Or am I...

So $$divE = \frac{1}{r}\frac{d}{d\psi}-\frac{1]{2}Kr^{n+1} = 0$$ It equals zero as K, r and n are constants and there is no psi component to differentiate. Thus the divergence being zero implies that it is rotational and therefore is not conservative so we can't define an electrostatic potential...

The question asks for just a few sentences as explanation which is throwing me off thinking they don't want me to do an operation on the E field to determine if the field is conservative by E=-gradV or to show CurlE=0. I'm assuming it can be done by inspection. I have this written down so far...

Homework Statement In a device called a betatron, charged particles in a vacuum are accelerated by the electric field E that necessarily accompanies a time-dependent magnetic field B(t). Suppose that, in cylindrical coordinates, the magnetic field throughout the betatron at time t can be...

Actually I think it shows that the magnetic field becomes zero in the hole when it is at the centre. Is this because of symmetry and cancelling?

Homework Statement Metal cylinder of radius a has the z-axis as its symmetry. It has magnetic field at any point P as: $$B[x,y,z] = \frac{1}{2} \mu_0 J_z [-ye_x + xe_y]$$ A cylindrical hole of radius b which is displaced from the cylinder's axis by d in the x direction. The magnetic field...

Also I'm not sure this question was posted in the right forum, if so could it be moved to the appropriate forum please, introductory or calculus perhaps?

I think I have the derivation part complete and I get $$B[r] = \frac {\mu_{o} I r}{2\pi a^2}e_{\phi}$$ Then since $$J = \frac{I}{\pi a^2}e_z$$ that substitutes in with J over ez giving me Jz. So then I just need to resolve the r and ephi into cartesian coordinates? Am I just substituting r for...

I am also trying to do this question. Just started this electromagnetism course and no sure where to stat with this question.