A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial...

2 months ago 1

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

$x = 0, y = 0, z = 0$ with a given initial velocity

\to v

$\vec{v}$ . A uniform electric field

\to E

$\vec{E}$ and a uniform magnetic field

\to B

$\vec{B}$ exist everywhere. The velocity

\to v

$\vec{v}$ , electric field

\to E

$\vec{E}$ and a uniform magnetic field

\to B

$\vec{B}$ are given in the columns below

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

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

(2) (i i) (R)

$(2) (i i) (R)$

(4) (i) (S)

$(4) (i) (S)$

(3) (i i) (R)

$(3) (i i) (R)$

(4) (i i) (R)

$(4) (i i) (R)$

Solution:

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 $(4) (i) (S)$ $(4) (i) (S)$ satisfy the condition. Path is helical with increasing pitch.

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A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial...

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IIT Madras

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IIT Kharagpur

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IIT Guwahati

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IIT Dhanbad

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IIT Jodhpur

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IIT Patna

Top Exams

A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial...

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