Question

We have three 0.5gram Styrofoam peanuts each with a charge of +3nC each separated by 0.1 meters. A 4th peanut is placed 20 cm above the right hand side peanut—it has a charge of -5nC.

a) Using analytical problem solving, what is the initial acceleration of the 4th peanut?

b) What is the E-field due to the 4 peanuts at a place 10 cm above the left-hand side peanut?

Answer 1

(a)

This is the setup

Now,

cos a = 0.2 / sqrt ( 0.2² + 0.1²)

cos a = 0.8944

and

cos b = 0.707

so,

in y- direction

Fy = 9e9 * 5e-9 ( 3e-9 / 0.2² + 3e-9 * 0.8944 / 0.05 + 3e-9 * 0.707 / 0.08)

Fy = 6.97e-6 N

In same way, In x - direction

Fx = 2e-6 N

so,

total net force

F = sqrt ( Fx² + Fy²)

F = 7.3e-6 N

so,

a = F / m

a = 0.0148 m/s²

_________________________

(b)

we know

r = sqrt ( 0.2² + 0.1² ) = 0.05

so,

E = 9e9 * -5e-9 / 0.05

E = -900 N/C