Question

Figure shows the path of an electron in a region of uniform magnetic field. The path consists of two straight sections, each between a pair of uniformly charged plates and two half-circles. The plates are named 1,2,3 and 4. Then

• A. 1 and 3 at higher (positive) potential and 2 and 4 at lower (negative) potential
• B. 1 and 3 at lower potential and 2 and 4 at higher potential
• C. 1 and 4 at higher potential and 2 and 3 at lower potential
• D. 1 and 4 at lower potential and 2 and 3 at higher potential

Answer 1

The correct option is C 1 and 4 at higher potential and 2 and 3 at lower potential

as shown in figure

$q=-ve\left(electron\right),\overrightarrow{\vartheta }=\vartheta (-\hat{i})$ and

$\overrightarrow{F}=F(-\hat{j})$

$\therefore$ using $\overrightarrow{F}=q(\overrightarrow{\vartheta }\ast \overrightarrow{B})$

$F(-\hat{j})=-e\vartheta (-\hat{i}\ast \overrightarrow{B})$

$F\hat{j}=-e\vartheta (\hat{i}\ast \overrightarrow{B})$

Hence direction of $\overrightarrow{B}$ must be along Z- axis (along $\hat{k}$)

In case of upper plates, to balance downward force by $\overrightarrow{B},\overrightarrow{E}$ must apply force upwards and hence plate 1 should be at higher, potential compared to 2.

Similarly in lower region, force acting by $\overrightarrow{B}$ is upward and hence to balance it plate 4 should be at higher potential compared to plate 3.