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 ( 0.2^{2} + 0.1^{2})

cos a = 0.8944

and

cos b = 0.707

so,

in y- direction

Fy = 9e9 * 5e-9 ( 3e-9 / 0.2^{2} + 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 ( Fx^{2} + Fy^{2})

F = 7.3e-6 N

so,

a = F / m

a = 0.0148 m/s^{2}

_________________________

(b)

we know

r = sqrt ( 0.2^{2} + 0.1^{2} ) = 0.05

so,

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

E = -900 N/C

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