A very long straight wire carries a current I. At the instant when a charge \[+\text{ }Q\] at point P has velocity \[\vec{v},\] as shown, the force on the charge is : |
[AIPMT (S) 2005] |
A) opposite to ox
B) along ox
C) opposite to oy
D) along oy
Correct Answer: D
Solution :
[d] Key Idea: At point P, Maxwell cork screw rule defines the direction of magnetic field and Fleming's left hand rule reveal the concept of force on the charge in this field. |
According to Maxwell's cork screw rule the direction of magnetic field at point P in plane of paper is perpendicular to the plane of paper inwards it., along z-direction. |
Now since charge is moving along x-direction therefore, from Fleming's left hand rule stretching the forefinger in direction of paper inwards the thumb will indicate the direction of force F acting on the charged particle along oy. |
Alternative: As discussed above, B acts inwards into plane of the paper and \[v\] is along of hence, |
\[F=Q(\vec{v}\times \vec{B}=Q\left| \begin{matrix} i & {\hat{j}} & {\hat{k}} \\ v & 0 & 0 \\ 0 & 0 & -B \\ \end{matrix} \right|\] |
\[=Q[\hat{i}(0)-\hat{j}(-vB)+\hat{k}(0)]\] |
\[=+\hat{j}QvB\] |
i.e., force is along oy direction. |
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