Question

A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed v_x. The length of plate is L and a uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL²/(2m v_x²).
(compare this motion with motion of a projectile in graviataional field as discussed in class 11 Physics. )

Solution

The particle is moving along x-axis in a uniformly charged electric field E between two oppositely charged metallic plates of length L. The motion of a charged particle in an electric field is analogous to the motion of a projectile in the gravitational field. The only difference is that here the constant electric field is in upward direction and is limited to the region between the plates of length L. Since x-component of the electric force is zero therefore, acceleration along x-axis is zero. So, the velocity v_x along x-axis is constant.

If x is the horizontal distance covered in time t, then

x = v_{x} t or t = \frac{x}{v_{x}}

Force acting along y-axis, F = qE

Acceleration along y-axis,

a_{y} = \frac{q E}{m}

where, m is the mass of charged particle (electron).

If y is the vertical distance covered by the particle in time t, then

y = u_{y} + a_{y} t^{2} [according to the equation of motion] y = \frac{1}{2} a_{y} t^{2} [∵ I n i t i a l v e l o c i t y i s z e r o]

\Rightarrow

y = \frac{1}{2} \frac{q E}{m} {(\frac{x}{v_{x}})}^{2}

∴

y = \frac{q E}{2 m v_{x}^{2}} x^{2}

So, within the electric field, the particle follows a parabolic path.

Let y, be the vertical deflection suffered by the particle inside the electric field.
When x = L, then

y = y_{1}

∴

y_{1} = \frac{q E L^{2}}{2 m v_{x}^{2}}

For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction