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(11) A high-energy pulsed laser emits a 1.0 -ns-long pulse of
average power $1.8 \times 10^{11}$ W. The beam is $2.2 \times 10^{-3}$ m in
radius. Determine $(a)$ the energy delivered in each pulse,
and $(b)$ the rms value of the electric field.

In this problem, I can write the value of average intensity of this solar radiation at ash desk, which is equal to PDS by four by required. On further simplification, I can write the expression for P does is equal to four pi R square multiplication. Al Death, which is equal to four pi multiplication, 1.5 multiplication. 10 to the power 11 m. Holy square multi pickets and 1390 What? Poor military square. On solving it further, I can write the value of Pds as the average power of the solar radius and edge three point 93 multiplication. 10 to the power 26. What as our final answer? I hope you understand how I solve this problem. I just use this simple formula and after that I just put all the value which are given in the question.

In this problem I can write individual fee is equal to design omega e minus X by sea. Yeah. He is not difficult to 50. That's why I like it like that now. He not is equal to under route. Who I by the nazi. So I'll bring it further. I can write the value as you notice square multiplication. E note C is equal to why one Further simplification. I can write the value of I is equal to you know, T square multiplication E. Multiplication. See by two solving it further I can write the value as high is equal to 50s. Where multiplication 8.85 multiplication tend to the power managed to will Multiplication three multiplication 8 by two Which is equal to 3.31. What parameters where co ops and see each correct answer.

Hello? Run. This is a solution to a problem. 30 Chapter 24 bottles. Physics. Um, in the first part of the problem, where s to find the electric and magnetic forces on a charge off? 2.6 times in three minutes. Eight crew arms, An electromagnetic wave that has an effort into intensity off 2.5 times 10 33 watts per meter squared. So how do we find the electric field? Well, electric field or the electric forces? Sorry, F yeah. Is equal to, uh que times the electric field. And so first, we need to find what the electric field is or we need to express the electric field in terms off the intensity. You know, that s or is equal to see absolute zero times e or M s squared. And so rearranging this for yeah, I find it is equal to or he or M s. Fergus, for the purpose of this problem is gonna be synonymous with, uh, with the So we have s bar over, See absolute zero square reading. So this is the value of PR mess. We're not going to work it out just yet. Instead, we're gonna do is realize that the particle is gonna be sitting here in the electric field is going to be pointing up so it doesn't really matter in which direction Thea the electric field is pointing is gonna be either pointing upward down. But magnitude off the force is with matters for purposes of this question. So we're going to say that the electric force is equal to, um it's gonna be equal to Q Times Square, right, as far over see absolute zero. And so when you work to sound, you find that the solution is to point far too 52 times 10 to the minus five Mutants were also asked to find what the magnetic forces or particle F B F B is given by a Q charge times the velocity of the particle, uh, crisp erected with the magnetic field B. But since particle in this port has no velocity, this is zero humans. So this is leaving the party, eh? This is slated to part B and that we're gonna end of velocity to it particle. And so we're going to a velocity of a particle this moving perpendicular to the magnetic field. So the directions are uh, over here. So electric field is moving on the vertical demand. Any field is moving into and out of the page, and velocity is moving left perpendicular to both the electric field and magnetic field. So the electric force Effie, is completely unaffected by the fact that the charges moving. So again, this is just Q We are a mess. So it's the same belly Ezri had before sits 2.52 times 10 titty minus five meetings. But now, Thea, the magnetic force is going to be different because the particle has velocity. Now, since the particles moving perpendicular to demean any field in the cross product, we can actually drop the sign factor. So we would have So we're just gonna have cute times. V times be, but so only so. But we don't know, be a safe yet, so we need to find would be is. But we do know that, um, yeah, or a miss for an electronic wave is related to, um be or I miss any field through this formula. So from this, we can work out that be, which is gonna be equivalent to B. R m s for our purposes here is equal to E. R. M s over, see, And so we can put all these values in now in this cue times V. Times or c times E or S begin substituting in the value for your mess from, uh, this part over here. It's just going to be Q times be oversee. There's Describe it off as bar over. See that zero force works out to be 3.11 times density, minus nine kids. So these are the solutions to part. See that party?

Hi. In the given problem, the equation of an electromagnetic way the magnetic director of the electromagnetic is given, as be set is equal to 3.0 micro Tesla into sign or one point Siegel into 10 days. Past seven X minus two by F. P. Now, if we compare it with a standard equation, B is, it is able to be not means magnitude means complete Europe Magnetic reversal. It will sign K X minus omega T. In the first part of the problem, we have to find Waveland, for which the skin is actually equal to do, buy, buy, land up. And here it's value is 1.0 into 10 past seven, so a Cleveland will be given by Dubai by 1.0 into 10 days Per 7 m means this is 6.28 into 10 days. Par minus 7 m means The answer for the first part of the problem means we've length of this electromagnetic wave is 6.28 into Standish Bar minus 7 m. The answer. For the first part of the problem. Now, in the second part of the problem, we have to find its frequency so again comparing we get omega equals to two by f so frequency here is simply is equal to f having no given value just in the terms of an unknown No. In the third part of the problem, we have to find the complete Europe electric field means not for which we use the relation the speed of the electromagnetic values given as the ratio of and played Europe electrical vector with the amplitude Europe magnetic vector. So the ski not be given by seeing to be not U C is equal to speed of light means three and do, and it's 48 per second into for the note. This is 3.0 micro Tesla of 3.0 into 10 days permanent six Tesla. So finally, this electric rules amplitude comes out to be 9.0 into 10 days, the power do world permit er or we can say this is not is equal to 900 vote four metre, which becomes the answer for the third and the last part of this problem. Thank you