A charged particle is introduced at the origin x = 0 , y = 0 , z = 0 with a given initial velocity v → . A uniform electric field E → and a uniform magnetic field B → exist everywhere. The velocity v

Question

A charged particle is introduced at the origin $x = 0, y = 0, z = 0$ with a given initial velocity $\vec{v}$ . A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$ , electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v}$ =0	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = - B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = - B_{0} \hat{z}$

In which case will the particle describe a helical path with axis along positive z direction?

TestHub · Accepted Answer

For path to be helix with axis along +ve z-direction, particle should experience a centripetal acceleration in x-y plane.

For the given set of options only option $(4) (i) (S)$ satisfy the condition. Path is helical with increasing pitch.

Physics - Magnetism Question with Solution | TestHub

Options:

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