Give definition of magnetic field and give its unit.
Give definition of magnetic field and give its unit.
Magnitude of force on electric charge in magnetic field is given by,
$\mathrm{F}=\mathrm{B} q u \sin \theta$ $\therefore \quad \mathrm{B}=\frac{\mathrm{F}}{q v \sin \theta}$
The magnitude of magnetic field $B$ is $1 \mathrm{SI}$ unit, when the force acting on a unit charge $(1 \mathrm{C})$,
moving perpendicular to $B$ with a speed $1 \mathrm{~m} / \mathrm{s}$ in one newton.
$SI$ unit:
Unit of $B$ $=\frac{\text { Unit of F }}{q v \sin \theta}$
$=\frac{1 \mathrm{~N}}{1 \mathrm{C} \times 1 \mathrm{~ms}^{-1} \times 1}=\frac{1 \mathrm{~N}}{1 \mathrm{Cs}^{-1} \times 1 \mathrm{~m}}$
$\quad=1 \mathrm{NsC}^{-1} \mathrm{~m}^{-1}$ is also called Tesla
$\quad=1 \frac{\mathrm{N}}{\mathrm{Am}}$
$\quad=1 \mathrm{NA}^{-1} \mathrm{~m}^{-1}=1 \mathrm{Tesla}$
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|
column $I$ |
column $II$ | column $III$ |
| $(I)$ Electron with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ | $(i)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0^2 \hat{\mathrm{Z}}$ | $(P)$ $\overrightarrow{\mathrm{B}}=-\mathrm{B}_0 \hat{\mathrm{x}}$ |
| $(II)$ Electron with $\overrightarrow{\mathrm{v}}=\frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{y}}$ | $(ii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{y}}$ | $(Q)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{x}}$ |
| $(III)$ Proton with $\overrightarrow{\mathrm{v}}=0$ | $(iii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{x}}$ | $(R)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{y}}$ |
| $(IV)$ Proton with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ | $(iv)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{\mathrm{x}}$ | $(S)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{z}}$ |
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$[A] (II) (iii) (S)$ $[B] (IV) (i) (S)$ $[C] (III) (ii) (R)$ $[D] (III) (iii) (P)$
($2$) In which case will the particle describe a helical path with axis along the positive $z$ direction?
$[A] (II) (ii) (R)$ $[B] (IV) (ii) (R)$ $[C] (IV) (i) (S)$ $[D] (III) (iii)(P)$
($3$) In which case would be particle move in a straight line along the negative direction of y-axis (i.e., more along $-\hat{y}$ )?
$[A] (IV) (ii) (S)$ $[B] (III) (ii) (P)$ $[C]$ (II) (iii) $(Q)$ $[D] (III) (ii) (R)$
- [IIT 2017]
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