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A straight wire lies along a body diagon...

A straight wire lies along a body diagonal of an imaginary cube of side `a=20 cm,` and carries a current of 5 A (as shown in Fig. 1.61). Find the force on it due to a uniform field `vec B = 0.6 hat j T.`

Text Solution

Verified by Experts

In order to use equation `vecF=iveclxxvecB`, we would need to find the
angle between `vecl and vecB`. We avoid this task by using unit vector
notation. Form the problem figure, we see that
`vecl=ahati-ahatj+ahatk`
Thus, the force is `vecF=IveclxxvecB=IaB(hati-hatj+hatk)xx(hatj)`
`=IaB(-hati+hatk)`
The force lies in the xz plane and has a magnitude
`F=sqrt2IaB=0.85N`
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