We'll start with the 6-step solution below and then follow-up with a more detailed explanation.
1) Let F_W = F_CFW=FC
2) F_C = 1/(4*pi*epsilon_0)*(q_1*q_2)/(r^2)FC=14⋅π⋅ε0⋅q1⋅q2r2
3) F_W=m*gFW=m⋅g
4) So re-write F_W =F_CFW=FC as
F_W = m*g =1/(4*pi*epsilon_0)*(q_1*q_2)/(r^2) = F_C FW=m⋅g=14⋅π⋅ε0⋅q1⋅q2r2=FC
5) (q_1*q_2)= m*g*(4*pi*epsilon_0)*(r^2)(q1⋅q2)=m⋅g⋅(4⋅π⋅ε0)⋅(r2)
6) Since q_1=q_2q1=q2, we can write q_1^2= m*g*(4*pi*epsilon_0)*(r^2)q21=m⋅g⋅(4⋅π⋅ε0)⋅(r2)
q_1^2=50kg*9.81m/s^2*(4*3.1415*8.854 * 10^-12F/m)*(10m)^2q21=50kg⋅9.81ms2⋅(4⋅3.1415⋅8.854⋅10−12Fm)⋅(10m)2
q_1^2=sqrt(5.45xx10^-6C^2)q21=√5.45×10−6C2
q_1=2.33xx10^-3Cq1=2.33×10−3C
...and we’re done!
1) The problem states that “the force between [the charges] equals the weight of a 50 kg person”. F_C = F_WFC=FW is a simple, way to express this mathematically, where F_CFC represents the force between the charges and F_WFW is the weight of the person.
2) F_CFC is the (electrostatic) force acting between two charges separated by a distance rr, where the magnitude of one of the charges is, q_1q1 and the magnitude of the other charge is q_2q2. epsilon_0ε0 is the electric permeability of free space.
3) F_W=m*gFW=m⋅g tells us that the weight of the person [or any object for that matter] is the mass of the object, mm, times the acceleration of gravity [due to the earth’s gravitational pull].
4) Here we expressed 1) in more explicit form, using equations 2) and 3)
5) The problem asks “What should be the magnitude of the charges”, so we rearrange equation 4) to solve for the charges, q_1*q_2q1⋅q2, by multiplying both sides by 4*pi*epsilon_0*r^24⋅π⋅ε0⋅r2.
6) The phrase “Two Equal charges” indicates that we can set q_2 = q_1q2=q1. In other words, the magnitude of each charge is the same. So q_1*q_2=q_1^2q1⋅q2=q21. After that, it’s just a matter of substituting the values for the quantities ( m,g,pi,epsilon_0 and rm,g,π,ε0andr ), carrying out a little arithmetic and we’re done!
