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The cube as shown in Fig. 1.61, 75.0 cm ...

The cube as shown in Fig. 1.61, 75.0 cm on a side, is placed in a uniform magnetic field of 0.860 T parallel to the x-axis. The wire abcdef carries a current of 6.58 A in the direction indicated.
(a) Determine the magnitude and direction of the force acting on the segment ab.
(b) Determine the magnitude and direction of the force acting on the sement bc.
(c) Determine the magnitude and direction of the force acting on the segment cd.
(d) Determine the magnitude and direction of the force acting on the segment de.
(e) Determine the magnitude and direction of the force acting on the segment ef.
(f) What are the magnitude and direction of the total force on the wire ?

Text Solution

Verified by Experts

(a) `vecF=Ivecl_(ab)xxvecB=I(l_(ab)B)hatjxxhati`
`=-(6.58A)(0.750m)(0.860m)hatk`
`=(-4.24N)hatk`
(b) `vecF=Ivecl_(bc)xxvecB=I(l_(bc)B)[(hati-hatk)/(sqrt2)xxhati]`
`=(6.58A)(0.750m)(0.860T)hatj`
`=(-4.24N)hatj`
(c) `vecF=Ivecl_(cd)xxvecB=I(l_(cd)B)[(hatk-hatj)/(sqrt2)xxhati]`
`=(6.58A)(0.750m)(0.860T)[hatj+hatk]`
`implies vecF=(4.24N)[hatj+hatk]`
(d) `vecF=Ivecl_(de)xxvecB=I(l_(de)B)[(-hatkxxhati)`
`=-(6.58A)(0.750m)(0.860T)hatj`
`=(4.24N)hatj`
(e) `vecF=Ivecl_(ef)xxvecB=I(l_(ef)B)(-hati)xxhati=0`
(f) Summing all the forces in parts (a)-(c), we have
`F_("total")=(-4.24N)hatj`
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