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 →

JEE Advanced 2017Paper 1

JEE Advanced 2017 · Paper 1 · Physics · Magnetic Effects of Current

A charged particle is introduced at the origin x = 0, y = 0, z = 0...

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

with a given initial velocity

\overset{\to}{v}

. A uniform electric field

\overset{\to}{E}

and a uniform magnetic field

\overset{\to}{B}

exist everywhere. The velocity

\overset{\to}{v}

, electric field

\overset{\to}{E}

and a uniform magnetic field

\overset{\to}{B}

are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\overset{\to}{v} = 2\dfrac{{E}_{0}}{{B}_{0}}\overset{^}{x}$	(i) $\overset{\to}{E} = {E}_{0}\overset{^}{z}$	(P) $\overset{\to}{B} = - {B}_{0}\overset{^}{x}$
2. Electron with $\overset{\to}{v} = 2\dfrac{{E}_{0}}{{B}_{0}}\overset{^}{y}$	(ii) $\overset{\to}{E} = - {E}_{0}\overset{^}{y}$	(Q) $\overset{\to}{B} = {B}_{0}\overset{^}{x}$
3.Proton with $\overset{\to}{v}$ =0	(iii) $\overset{\to}{E} = {- E}_{0}\overset{^}{x}$	(R) $\overset{\to}{B} = - {B}_{0}\overset{^}{y}$
4. Proton with $\overset{\to}{v} = 2\dfrac{{E}_{0}}{{B}_{0}}\overset{^}{x}$	(iv) $\overset{\to}{E} = {E}_{0}\overset{^}{x}$	(S) $\overset{\to}{B} = - {B}_{0}\overset{^}{z}$

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

B. $( 4 ) ( i ) ( S )$

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.