A charged particle having charge q and mass m accelerated by a potential difference $V_{0}$ enters inside a parallel plate capacitor (parallel to length l of plates) at mid-point of its separation between plates at $t = 0$ . Potential difference across capacitor varies with time t as, $V = a d t,$ where a is constant and d is separation between plates. Angle of deviation as it comes out of plates, is $\frac{π}{4}$ . Value of $\frac{m a^{2} I^{4}}{2 q V_{0}^{3}}$ , will be

Open in App

Solution

Horizontal distance

$l = V_{x} t,$

Velocity of charge particle in x- direction

$V_{x} = \sqrt{\frac{2 q V_{0}}{m}}$

Acceleration of charge particle is given as

$a = \frac{q E}{m}$

Velocity of charge particle in y- direction

$V_{y} = \int \frac{q E}{m} d t$

$= \frac{q}{m} at d t$

$V_{y} = \frac{q}{m} a \frac{t^{2}}{2}$

$V_{y} = \frac{q}{m} a \frac{l^{2}}{2 V_{x}^{2}}$

$= \frac{q a I^{2}}{2 m} (\frac{m}{2 q V_{0}})$

$V_{y} = \frac{a l^{2}}{4 V_{0}}$

$tan θ = \frac{V_{y}}{V_{x}} = \frac{a l^{2}}{4} \sqrt{\frac{m}{2 q V_{0}^{3}}}$

Suggest Corrections

Similar questions

Q. The separation between the plates of a charged parallel-plate capacitor is increased. Which of the following quantities will change?
(a) Charge on the capacitor
(b) Potential difference across the capacitor
(c) Energy of the capacitor
(d) Energy density between the plates

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ , with a potential difference $V$ between the plates, is:

Q. 169 A parallel plate capacitor having a plate area A and plate separation d is joined to a battery of emf Even and internal resistance R at t=0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Define displacement resistance Rd=V/id (where id is displacement current) of the space between the plates where V is the potential difference between the plates. Show that Rd varies with time as

Q. A parallel plate capacitor has plate area

A

and separation

d

. It is charged to a potential difference

V_{0}

. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is:

Q. A parallel plate air capacitor has capacity

^{'} C^{'}

, distance of separation between plate is

^{'} d^{'}

and potential difference

^{'} V^{'}

is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is:

Join BYJU'S Learning Program

Horizontal distance l=Vxt, Velocity of charge particle in x- direction Vx=√2qV0m Acceleration of charge particle is given as a=qEm Velocity of charge particle in y- direction Vy=∫qEmdt =qm at dt Vy=qmat22 Vy=qmal22V2x =qaI22m(m2qV0) Vy=al24V0 tanθ=VyVx=al24√m2qV30