An electron moves with speed $2 \times {10^5}\,m/s$ along the positive $x$-direction in the presence of a magnetic induction $B = \hat i + 4\hat j - 3\hat k$ (in $Tesla$) The magnitude of the force experienced by the electron in Newton's is (charge on the electron =$1.6 \times {10^{ - 19}}C)$
Medium
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(c) $\overrightarrow {v\,} = 2 \times {10^5}\hat i $and $\overrightarrow B = (\hat i + 4\hat j - 3\hat k)$
$\overrightarrow F = q\,(\overrightarrow {v\,} \times \overrightarrow B ) = - 1.6 \times {10^{ - 19}}[2 \times {10^5}\hat i \times (i + 4\hat j - 3\hat k)]$
$ = - 1.6 \times {10^{ - 19}} \times 2 \times {10^5}[\hat i \times \hat i + 4(\hat i \times \hat j) - 3(\hat i \times \hat k)]$
$ = - 3.2 \times {10^{ - 14}}[0 + 4\hat k + 3\hat j] = 3.2 \times {10^{ - 14}}( - 4\hat k - 3\hat k)$
$==>$ $|\overrightarrow F |\, = 3.2 \times {10^{ - 14}} \times 5 = 1.6 \times {10^{ - 13}}N.$
$\overrightarrow F = q\,(\overrightarrow {v\,} \times \overrightarrow B ) = - 1.6 \times {10^{ - 19}}[2 \times {10^5}\hat i \times (i + 4\hat j - 3\hat k)]$
$ = - 1.6 \times {10^{ - 19}} \times 2 \times {10^5}[\hat i \times \hat i + 4(\hat i \times \hat j) - 3(\hat i \times \hat k)]$
$ = - 3.2 \times {10^{ - 14}}[0 + 4\hat k + 3\hat j] = 3.2 \times {10^{ - 14}}( - 4\hat k - 3\hat k)$
$==>$ $|\overrightarrow F |\, = 3.2 \times {10^{ - 14}} \times 5 = 1.6 \times {10^{ - 13}}N.$
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