Question

An electron starting from rest takes 14x10-9 sec to reach from one plate to
other of a capacitor placed 2 cm apart. If charge to mass ratio of electron
is 1.8x1011 CI kg. Then find the potential difference between the plates.​

Answer 1

Given info : An electron starting from rest takes 14 × 10^-9 sec to reach from one plate to other of a capacitor placed 2 cm apart. If charge to mass ratio of electron is 1.8x10¹¹ C/kg

To find : the potential difference between the plates is ...

solution : during the motion of electron from one plate to the other, at a point,

electrostatic force = ma

⇒qE = m(v - u)/t

as it starts from rest so, u = 0

⇒qE = mv/t

⇒(q/m)t = v/E

⇒(q/m)t = (∆x/t)/E

⇒(q/m)t² = ∆x/E

we know, potential difference, ∆v = E.∆x

⇒(q/m)t² = ∆x²/∆v

now, q/m = 1.8 × 10¹¹ C/kg , t = 14 × 10^-9 sec , ∆x =2cm = 0.02 m

⇒(1.8 × 10¹¹)(14 × 10^-9)² = (0.02)²/∆v

⇒352.8 × 10^-7 = 4 × 10^-4/∆v

⇒84.7 × 10^-3 = 1/∆v

⇒∆v = 10³/(84.7) = 11.8 Volts

Therefore the potential difference between the plates is 11.8 volts