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capa 10 - Phys 1120 CAPA#10 solutions 1 This problem is...

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Phys 1120, CAPA #10 solutions. 1) This problem is about B fields from wires -BOTH wires produce B-fields at ALL points in space. So when you look at, say, point p1, it receives contributions from the upper and lower wire. In this case (since the currents go in opposite directions, those fields will also go in opposite directions, that's how it's possible to get the field to be 0 down there at point p1!) The point p1 is "a" from the lower wire, and "3a" from the upper wire. Using the right hand rule, the B field due to wire I1 will be INTO the page down there where p1 is. The B field due to wire I2 will be OUT of the page down there where p1 is. (Convince yourself, don't just take my word for it!! If you don't know how to find the direction of B, please ask someone, it's hard to write but easy to show with fingers! see Fig 32.14 to remind yourself of the basic picture. ) So, the fields can cancel. Formula-wise B1 = mu0 I1 / (2 pi (3a)) IN. B2 = mu0 I2/ (2 pi (a)) OUT. In order for the field to vanish, those two must be equal in magnitude, so I1/3a = I2/a, or I1 = 3 I2. They gave us I2, so just triple it to find I1. (Makes sense, I1 is three times farther away, so the current needs to be 3 times bigger to give an equal field, which is what you need to get cancellation!) 11) In the middle, at point P2, the B field due to I1 is still into the page, but the B field due to I2 is now ALSO into the page. (We're now ABOVE wire 2). Again, convince yourself! In the "in between" region, the two B fields add, they don't cancel. So we have B1 + B2 = muo (I1 + I2)/(2 pi a) (where, in this formula, I really mean the magnitude of I1 and the magnitude of I2, I've already accounted for their directions when I worked out that they add up) Since I1 = 3I2, we have mu0*4I2/(2 pi a) ( Just plug in for CAPA) 3) Magnetic fields form circular loops around currents, in the "right hand sense". (See e.g. Fig 32.14 in your text). In this case that means B at point p1 points SOUTH (down the page), and the same at p2 (but, weaker, because it's farther away) An electron at REST will feel no magnetic force (you have to be moving to feel a force!) 4) Since B = mu0*I/(2 pi r), if you are twice as far away, the B field is half as strong. (It varies inversely as radius, not radius squared or anything) So, depending on which point was given to you (p1 or p2) just divide or multiply the number given by two! 5) I = dq/dt. Here, dq = 15 C (your number might vary), and dt = 1.5E-3 sec, so I = 15/1.5E-3 A = 10^4 Amps. (Big current!) Now just use the formula 30-5 of your text (same as 30-8), B = mu0*I/ (2 pi r). We just got I, mu0 is a constant, r is given. The answer comes out pretty small - magnetic fields TEND to be small in nature, unless something rather unusual is going on (it's hard to get "1 Tesla" fields!)
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6) A) The long wire generates a B field around itself (RHR #1) which circles around the long wire, and thus points OUT of the plane of the paper everywhere in the picture, in particular, everywhere along the smaller wire.
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