A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial...
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
In which case will the particle move in a straight line with a constant velocity?
Column 1 | Column 2 | Column 3 |
1. Electron with →v=2E0B0ˆx | (i) →E=E0ˆz | (P) →B=-B0ˆx |
2. Electron with →v=E0B0ˆy | (ii) →E=-E0ˆy | (Q) →B=B0ˆx |
3.Proton with →v =0 | (iii) →E=-E0ˆx | (R) →B=-B0ˆy |
4. Proton with →v=2E0B0ˆx | (iv) →E=E0ˆx | (S) →B=-B0ˆz |
Solution:
Given: A charged particle is introduced at the origin (x=0,y=0,z=0). initial velocity =→v,
uniform electric field →E.
uniform magnetic field →B.
Also the values are given the table.
we need to find the cases where the particle will move in a straight line with constant velocity.
To move a particle with constant velocity;
Fnet =0,
⇒ The electric force = magnetic fore e.
qE=qvB.E=vB.
Now checking the options.
A) (II) (iii) (s). (II) =→v=E0B0ˆy. (iii) =→E=−E0ˆx(s)=→B=B0ˆZ. −E0ˆx=E0^BOˆy(BOˆz)
∴ (II) (iii) (s) is the correct option
uniform electric field →E.
uniform magnetic field →B.
Also the values are given the table.
we need to find the cases where the particle will move in a straight line with constant velocity.
To move a particle with constant velocity;
Fnet =0,
⇒ The electric force = magnetic fore e.
qE=qvB.E=vB.
Now checking the options.
A) (II) (iii) (s). (II) =→v=E0B0ˆy. (iii) =→E=−E0ˆx(s)=→B=B0ˆZ. −E0ˆx=E0^BOˆy(BOˆz)
∴ (II) (iii) (s) is the correct option
Join the conversation