Discussion
A unit charge q moving with initial velocity \((\overline{v} = v_{x}\hat{i})\) is subjected to external electric field \((\overline{E} = E_{y}\hat{j})\). The number of degrees of freedom is :
Answer: B
The motion has 2 degrees of freedom.
The charge starts with velocity along \(\hat{i}\) and the only force, \(q\overline{E}\), acts along \(\hat{j}\). Nothing ever gives it a velocity component along \(\hat{k}\), so the motion stays in the x-y plane: it moves uniformly in x and accelerates in y, tracing a parabola.
Two independent coordinates, x and y, are needed to describe it, so the number of degrees of freedom is 2. A free particle in space would have 3, motion along a line 1, and zero would mean no motion at all.
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