The bent wire shown in Fig. 28 42 lies in a uniform magnetic...

The bent wire shown in Fig. 28 42 lies in a uniform magnetic field. Each straight section is $2.0 \mathrm{~m}$ long and makes an angle of $\theta=60^{\circ}$ with the $x$ axis, and the wire carries a current of $2.0 \mathrm{~A}$. What is the net $\mathrm{mag}$ netic force on the wire in unit-vector notation if the magnetic field is given by (a) 4.0k T and (b) 4.0\hat T?

Transcript

00:01 So in this problem we have bent wire, which is divided into two pieces, piece number one and piece number two.

00:09 Piece number one is making an angle of theta, which is equal to 60 degrees with the negative x -axis, counter -cliquise.

00:17 And the angle that wire 2 is making with the positive x -axis, click -wise is also theta, which is equal to 60 degrees.

00:26 Every part of the wire is two meters long and the current in the wire is two amperors so here for part a we have a magnetic field b which is uniform and this is equal to four teslas in the positive z direction and we need to get the total magnetic force on the total wire so here f1 which is the magnetic force vector on the third part of the wire and this is equal to i l1 vector cross b and here l1 is equal to to cosine of theta i hat plus two sign of theta j hat so here f1 is equal to i which is two multiplied by 2 cosine of theta i -hat plus 2 sine of theta j -hat and this is cross b which is 4 k -hat so this is equal to 16 times cosine of theta i hat plus sine of theta i hat plus sine of theta j hat cross k hat and this is equal to minus 16 cosine of theta j hat plus 16 sine of theta i hat so this is f1 and now we get f2 which is the magnetic force on the second part of the wire and this is equal to i l2 cross b and here here l2 is equal to 2 cosine of theta i hat minus 2 sine of theta j hat so here f2 is equal to 2 times 2 cosine of theta i hat minus 2 sine theta j hat cross the magnetic field which is 4 k hat and this is equal to 16 times cosine of theta i hat minus sign of theta j hat cross k hat so this is equal to minus 16 cosine of theta j hat so this is f2 now the total magnetic force on the wire is if total magnetic force on the wire is if total and this is equal to f1 plus f2 and this is equal to minus 32 cosine of theta j hat and this is equal to minus 60 degrees j hat and this is equal to minus 16 newton's j hat...

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