Recent content by diethaltao

Homework Statement A plane monochromatic electromagnetic wave with wavelength λ = 2.2 cm, propagates through a vacuum. Its magnetic field is described by \vec{B} = (Bx\vec{i} + By\vec{j})cos(kz+ωt) where Bx = 1.8E-6 T and By = 3.8E-6 T, and i-hat and j-hat are the unit vectors in the +x and...

Oh, wow, I get it now. Can't believe I overlooked something so simple! Thanks so much! :smile:

Ok, I understand that. So now I have something like the picture attached, where R is the hypotenuse of a 0.21 by 0.21 triangle (not sure if I need that value, but I calculated it anyways.) The integral from P to S is the same as the integral of T to S. And therefore, the integral from P to T...

Hi tiny-tim! Ampere-Maxwell's law says that \vec{B}.\vec{dL} around a closed loop is proportional to the current enclosed in that loop, or \oint\vec{B}.\vec{dL} = μo*Ienc. But I can't just plug in the values of μo and Ienc to solve for the integral. And if I choose a square to be my...

Hi tiny-tim! So, I would find r using the Pythagorean Theorem: r = \sqrt{((0.21)(0.6))^2+(0.21-(0.21)(0.6))^2} = 0.151. So I would multiply the field (which I found at point P to be 4.19E-6) by the perimeter of the square? And the perimeter would be 8R...? Obviously I messed up somewhere.

Homework Statement A solid cylindrical conducting shell of inner radius a = 5.3 cm and outer radius b = 7.9 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 7.1 A in the positive z-direction. An infinite conducting wire is located along the...

Ah, whoops! To find potential, you integrate electric field. E = (Qouter + Qinner)/(4πεo) ∫dr/(r^2) from infinity to c, and add that to E = (Qinner)/(4πεo) ∫dr/(r^2) from b to a? So potential would be: (Qouter + Qinner)/(4πεo) * (1/c) + (Qinner)/(4πεo) * ((1/a)-(1/b)) But I don't understand...

Ah, ok. I understand this much more. Hopefully I'll do well on my midterm tomorrow. Thanks again!

Sorry, that expression was supposed to be what I thought would find the potential for the outer surface of the insulating sphere. Potential outside the sphere would just be the Qenclosed divided by 4πεo times the integral dr/r, right? (0.00724μC + ρV)/(4πεo) * ln(r)?

Thank you so much! All of these integrals and concentric shells are really confusing. If I just wanted to find the electric potential on the outer surface of the cylindrical shell, would I just do λ/(2πεo)*ln(a)? Or would I have to account for the charge of the charge of the surrounding...

So if I make the Gaussian surface b < r < c, the Qenclosed equals zero, which means that the inner surface of the conducting shell will be equal in magnitude but opposite in direction of Q1? Q3 would be Q1+0.0724μC? So would I sum up the charges and their distances like: kQ3((1/c)-(1/a))...

Homework Statement A solid insulating sphere of radius a = 5.6 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -159 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 10.7 cm, and...

Thanks! λ is charge per unit length or coulombs per meter, correct? I know that λL = Qenclosed, but I'm not sure what to do if it is infinitely long. Or does the L cancel off if we write: E2πrL = Qenclosed/εo = λL/εo Which can be simplified to: E = λ/(2πrεo)? And I could take the integral of...

Homework Statement An infinitely long solid conducting cylindrical shell of radius a = 3.1 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.49 μC/m. Concentric with the shell is another...