Question
A charge moving with velocity $$v$$ in $$x$$-direction is subjected to a field of magnetic induction in negative $$x$$-direction. As a result, the charge will
A.
remain unaffected
B.
start moving in a circular $$y$$ - $$z$$ plane
C.
retard along $$x$$-axis
D.
move along a helical path around $$x$$-axis
Answer :
remain unaffected
Solution :
Force on a charged particle in the magnetic field is
$$\left| F \right| = q\left| {v \times B} \right|\,\,{\text{or}}\,\,F = qvB\sin \theta $$
when angle between velocity $$v$$ and magnetic induction $$B$$ is $${180^ \circ }$$ or $${0^ \circ },$$ then
$$F = qvB\sin {180^ \circ } = 0\,\,\left[ {{\text{as}}\,\sin {{180}^ \circ }\,{\text{or}}\,\sin {0^ \circ } = 0} \right]$$
So, the charged particle remains unaffected.
Force on a charged particle in the magnetic field is
$$\left| F \right| = q\left| {v \times B} \right|\,\,{\text{or}}\,\,F = qvB\sin \theta $$
when angle between velocity $$v$$ and magnetic induction $$B$$ is $${180^ \circ }$$ or $${0^ \circ },$$ then
$$F = qvB\sin {180^ \circ } = 0\,\,\left[ {{\text{as}}\,\sin {{180}^ \circ }\,{\text{or}}\,\sin {0^ \circ } = 0} \right]$$
So, the charged particle remains unaffected.