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  4. A uniform electric field of 10 N / C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle (θ) of deviation of the path of electron as it comes out of the field is (in degree).

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Q. A uniform electric field of $10\, N / C$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy $0.5 \,eV$. The length of each plate is $10\, cm$. The angle $(\theta)$ of deviation of the path of electron as it comes out of the field is ___ (in degree).Physics Question Image

JEE MainJEE Main 2023Electric Charges and Fields

Solution:

$0.5 e =\frac{1}{2} mv _{ x }^2 \Rightarrow v _{ x }=\sqrt{\frac{ e }{ m }}$
Along $x L = v _{ x } t =\sqrt{\frac{ e }{ m } t }$
Along $y v _{ y }=\frac{ eE }{ m } t$
$\operatorname{dividing} \frac{ v _{ y }}{ L }= E \sqrt{\frac{ e }{ m }}= Ev _{ x }$
$\Rightarrow \operatorname{Tan} \theta=\frac{ v _{ y }}{ v _{ x }}= E \times L =10 \times 0.1=1$
$\theta=45^{\circ}$