Question 1 : In the figure particle 1 of charge +4 e is above a floor by distanc

Question

Question 1: In the figure particle 1 of charge +4e is above a floor by distance d1 = 2.80 mm and particle 2 of charge +6e is on the floor, at distance d2 = 9.00 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1?

Question 2: In the figure four particles are fixed along an x axis, separated by distances d = 4.00 cm. The charges are q1 = +3e, q2 = -e, q3 = +e, and q4 = +8e, with e = 1.60 × 10-19 C. What is the value of the net electrostatic force on (a) particle 1 and (b) particle 2 due to the other particles?

Question 3: Two small, positively charged spheres have a combined charge of 36.0 × 10-5 C. If each sphere is repelled from the other by an electrostatic force of 0.700 N when the spheres are 1.70 m apart, what is the charge on the sphere with the smaller charge?

Plz i need the answer for the 3 questions

Explanation / Answer

d21 = sqrt(d2^2 + d1^2) = sqrt(9.0^2 + 2.8^2)mm = 9.425 mm = 0.009425 m

F21 = k*q2*q1/d21^2 = 8.99*10^9*6*4*(1.6*10^-19)^2 / 0.009425^2

F21 = 6.218x10^-23 N

F21 is at angle arctan(2.8/9.0) below the horizontal = 17.28 degrees

So x component of F21 is 6.218*cos(17.28) * 10^-23 N = 5.937*10^-23 N

2.

Force from q2 on q1 = k(e)(-e)/d^2 (The force on q1 is attraction; it acts to the right)
Force from q3 on q1 = k(e)(e)/(2d)^2 (The force on q1 is repulsion; it acts to the left)
Force from q4 on q1 = k(e)(4e)/(3d)^2 (The force on q1 is repulsion; it acts to the left)

Add the 3 forces on q1, making the values +ve if to the right and negative if to the left

Force on q1 = [k(e)(e)/0.04^2] [ +1 -1/4 - 4/9]
= [8.99E9 x (1.60E-19)^2 / 0.04^2] x 0.306
= 4.406E-26

3.

The force between the spheres is

F = kQ1Q2/d^2 = 8.98*10^9 Vm/(As) * Q1*Q2/1.70^2 = 0.70
and Q1+Q2 = 36*10^-5 C

or 0.70 = 3.114x10^9*Q1*(36x10^-5 -Q1)

or 3.114x109 Q12 -1.12x10^6*Q1 + 0.70 =0

bys olving quadratic equation

Q1 =

The solutions for Q1 and Q2 are
Q1 =6.26*10^-6 C
Q2 = 35.374*10^-5 C

The smaller charge is 6.26*10^-6 C

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