Magnetics Ques 26
Match the Columns
Matching the information given in the three columns of the following table.
A charged particle (electron or proton) is introduced at the origin $(x=0, y=0, z=0)$ with a given initial velocity $\mathbf{v}$. A uniform electric field $\mathbf{E}$ and a uniform magnetic field $\mathbf{B}$ exist everywhere. The velocity $\mathbf{v}$, electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$ are given in columns $1, 2$ and $3$, respectively. The quantities $E _0, B _0$ are positive in magnitude.
| Column 1 | Column 2 | Column 3 | ||
|---|---|---|---|---|
| (l) | Electron with $v=2 \frac{E _0}{B _0} \hat{x}$ |
(i) | $E=E _0 \hat{z}$ | (P) $B=-B _0 \hat{x}$ |
| (II) | Election with $v=\frac{E _0}{B _0} \hat{y}$ |
(ii) | $E=-E _0 \hat{y}$ | (Q) $B=B _0 \hat{x}$ |
| (III) | Proton with $v=0$ |
(iii) | $E=-E _0 \hat{x}$ | (R) $B=B _0 \hat{y}$ |
| (IV) | Proton with $v=2 \frac{E _0}{B _0} \hat{x}$ |
(iv) | $E=E _0 \hat{x}$ | (S) $B=B _0 \hat{z}$ |
(2017 Adv.)
- In which case will the particle move in a straight line with constant velocity?
(a) (II) (iii) (S)
(b) (III) (iii) (P)
(c) (IV) (i) (S)
(d) (III) (ii) (R)
Show Answer
Answer:
Correct Answer: 26.(a)
Solution:
Formula:
Magnetic Force Acting On A Moving Point Charge:
- $\quad \mathbf{F} _{\text {net }}=\mathbf{F} _e+\mathbf{F} _B=q \mathbf{E}+q \mathbf{v} \times \mathbf{B}$
For particle to move in straight line with constant velocity,
$\mathbf{F} _{\text {net }}=0$
$\therefore q \mathbf{E}+q \mathbf{v} \times \mathbf{B}=0$
BETA
