Question

an electron is projected into a uniform electric field of strength 2000N/C with initial velocity 10^6 m/s perpendicular to the field what is the ratio of electric force and its weight +

Answer 1

AnswEr :

Given :

• An electron is projected into an Uniform Electric Field

• The magnitude of 'E' is 2000 N/C

We know that,

• Charge on an Electron = - 1.6 × 10^-19 C

• Mass of an Electron = 9.1 × 10^-31 C

• Acceleration due to gravity is 10 m/s²

To finD

The Ratio of Electrostatic Force and Weight .

Now,

Electric Field is given as :

$\rm E = \dfrac{F}{Q} \\ \\ \longrightarrow \rm F = E \times Q \\ \\ \longrightarrow \boxed{\boxed{\rm F = - 3.2 \times 10^{-16} \ N }}$

Weight would be expressed as :

$\rm W = Mg \\ \\ \longrightarrow \rm W = (9.1 \times 10^{-31}) \times 10 \\ \\ \longrightarrow \boxed{\boxed{\rm W = 9.1 \times 10^{-30} \ N}}$

Therefore,

Ratio of Weight and Electrostatic Force :

$\sf \dfrac{F}{W} = - \dfrac{3.2 \times 10^{-16}}{9.1 \times 10^{-30}} \\ \\ \implies \sf \dfrac{F}{W} = - \dfrac{320 \times 10^{13}}{91} \\ \\ \large{\implies \ \boxed{\boxed{\sf F : W = - 3.51 × 10^{31} : 1 }}}$

Electrostatic Force is 3.51 × 10¹³ times the Weight of the Electron

Answer 2

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QUESTION -

An electron is projected into a uniform electric field of strength 2000N/C with initial velocity 10^6 m/s perpendicular to the field .

What is the ratio of electric force and its weight ??

SOLUTION -

We know that :

Electric Force = Electric Field × Charge

Let the charge of the electron be Q.

So,

F = [ 2000 Q ] N.

Weight = Mass × Acceleration Due to gravity.

So,

$\dfrac{Electric \: Force }{ Weight } = \dfrac{ 2000 Q }{ mg }$

Note that I have kept the ratio in terms of Constants, as the exact value varies.