Ask your homework questions to teachers and professors, meet other students, and be entered to win $600 or an Xbox Series X 🎉Join our Discord!

Like

Report

Numerade Educator

Like

Report

Problem 51 Hard Difficulty

(III) Suppose a uniformly charged wire starts at point 0 and rises vertically along the positive $y$ axis to a length $\ell$ . (a) Determine the components of the electric field $E _ { x }$ and $E _ { y }$ at point $( x , 0 ) .$ That is, calculate $\vec { \mathbf { E } }$ near one end of a long wire, in the plane perpendicular to the wire. (b) If the wire extends from $y = 0$ to $y = \infty ,$ so that $\ell = \infty ,$ show that $\vec { \mathbf { E } }$ makes a $45 ^ { \circ }$ angle to the horizontal for any $x .$ [Hint: See Example 11 of "Electric Charge and Electric Field" andFig. $29 . ]$

Answer

A. $\frac{\lambda}{4 \pi \varepsilon_{0} x \sqrt{x^{2}+\ell^{2}}}(x-\sqrt{x^{2}+\ell^{2}})$
B. $45^{\circ}$ below the $x$ axis

Discussion

You must be signed in to discuss.
Top Physics 102 Electricity and Magnetism Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Other Schools

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp

Video Transcript

All right. So we have a white here letting since from a way, for the jury to L We are interested in cooperating the components off little free lead. Partygoer point B. All right, So for that we consider a small sex and your wife along the wire that Charleston for Machar's. Now there's first Fine, uh, feel small leap accredited to this small cross section that is a D Did you call to key chimes? The charged the ass charge that contained in Dubai is Lambda Time still white charge violet linen to fill in upon the distance is he's sorry. Square right. I s body's excess current this waste where now do it has two components to costed out alone X axis on desire The Y axis so excites d e x is going to g e Caustic now hostage are in the figure from the triangle caustic and religion as based off unhappiness So base He's ex on hyper Chinese He's rude tender It's e squared plus y squared So what we can, right? If you combine the best person for de year, this would give me Kay Landa eggs Do you buy Born the squire plus ways wire on dhe is because three by two. All right, now similarly, the complainant alone do you? Why that is you lied would become with the same process you have signed. Return it so that scientists have you knew why up one older and directors weapons. Why square so this person would be gain them. Not like you. A port. It's he squired less. Why swear? Power three up to right. So found. But since you why is the own worst? I can write this as a negative. All right, so, uh, totally quit along X axis. So e x is what it is. The integration off D e X chrome the world end of the wire. Right. So this becomes G. Amanda. Eggs are independent off. Why? So I can dig them out so I can take hours so that we can ski lambda x outside on dde Gino to l from you're on. Dangerous enough. Actually, square lasts twice. Power three or 12 Andi, this with respect to do you write right now you're usin off. This can be seen dependents on that dips move kill under X times into Kristen. He's why, upon exes squired grew tender. It is worth less. Why swear from zero to right. So if you plug in the hell and Jiro here and some practice on, so do the value for Lambda this the gums manager? Oh, one or by upset. A lot X route over X square. Plus it's quiet. Well, we're done. We are done with this. Now you have that, Grady? Yeah, X, right. It means give this in a box. Okay, Now, similarly, we calculate you why your wife is doing curating again, Geo to help. Now, In this case, only kill Amanda was also key Landa from enjoying too. Oh, that would be Why do you lie on? It's just a heartless my squire. Our three by two. Right now this is equal to If you regret this by the Knicks, this chance are to be minus. Gave him, um, skin landa This view one on or gender exist Squired plus wise wired. Oh, Gero too, huh? Right, right. So I missed a negative sign here. Yeah, so the next you can do is blocking the values. Are general this next bit Lando? One for by I said I'm not, but on if you take the else him off the animators and and solve the Franks is there. So this will be out scar plus the square of the new manager. We have X minus gender XY squared less, squire. All right, so this is the value for you. What? All right now we are. Don't you a party of the question. Now, let's move on to part B. I hope I can do in this little space here, but the of the question I don't want to use next face because I need to use the Formalized you and he x here. So to find that the little film, it's an end of 45 degree. I'll just find the entry angle bursts of them. Peter is equality. Five years, Right? So that is, uh called, too. If you divide, you might buy PX. We have all the denominator in common, right? So we only have left. You're either the X when you had x minus route tender. Actually, squire less any squire upon Oh, so this separated of Braxton's here? That's my l minus root Ginger one plus thanks. Bye. Oh, what? No. Ready, then. Elbows to infinity. This means Dan Kita exit so exciting thingies. Uh, general, So explain pretties again. Generals, that give me minus one. This is a place he dies. He will do what you have to be down Wash writes a minus 45 degrees. Since you guys down worse so we can write the angle that electric field medics XX is is 45 degrees John Worse. All right, so we are done with part B of the problem as well. So this wasp art be on this last part 80 as a whole. So thank you for watching where it

Kansas State University
Top Physics 102 Electricity and Magnetism Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Other Schools

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp