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…

Question

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→ , electric field E→ and a uniform magnetic field B→ are given in the columns below Column 1 Column 2 Column 3 1. Electron with v→=2E_0/B_0x^ (i) E→=E_0z^ (P) B→=-B_0x^ 2. Electron with v→=2E_0/B_0y^ (ii) E→=-E_0y^ (Q) B→=B_0x^ 3.Proton with v→ =0 (iii) E→=-E_0x^ (R) B→=-B_0y^ 4. Proton with v→=2E_0/B_0x^ (iv) E→=E_0x^ (S) B→=-B_0z^ In which case would the particle move in a straight line along the negative direction of y axis

MARKS Content Team · Accepted Answer

Correct answer: (D) (3) (ii) (R). For particle to move in -ve y-direction, either its velocity must be in –ve y-direction (if initial velocity ≠ 0) and force should be parallel to velocity or it must experience a net force in –ve y-direction only (if initial velocity = 0)

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) $\vec{B} = - B_{0} \hat{z}$

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