Question

A small glass bead has been charged to 20 nC. What is the magnitude of acceleration in m/s^2 of an electron that is 1.0 cm from the center of the bead? (mass of an electron= 9.1x10^-31 kg)

Answer 1

The acceleration is 3.16x10¹⁷ m/s².

Step-by-step explanation:

First, we need to find the magnitude of the Coulombs force (F):

`|F| = (Kq_(1)q_(2))/(d^(2))`

Where:

K is the Coulomb constant = 9x10⁹ Nm²/C²

q₁ is the charge = 20x10⁻⁹ C

q₂ is the electron's charge = -1.6x10⁻¹⁹ C

d is the distance = 1.0 cm = 1.0x10⁻² m

`|F| = (Kq_(1)q_(2))/(d^(2)) = (9\cdot 10^(9)Nm^(2)/C^(2)*20 \cdot 10^(-9) C*(-1.6\cdot 10^(-19) C))/((0.01 m)^(2)) = 2.88 \cdot 10^(-13) N`

Now, we can find the acceleration:

`a = (F)/(m) = (2.88 \cdot 10^(-13) N)/(9.1 \cdot 10^(-31) kg) = 3.16 \cdot 10^(17) m/s^(2)`

Therefore, the acceleration is 3.16x10¹⁷ m/s².

I hope it helps you!