We'll start with the 6-step solution below and then follow-up with a more detailed explanation.
1) Let #F_W = F_C#
2) #F_C = 1/(4*pi*epsilon_0)*(q_1*q_2)/(r^2)#
3) #F_W=m*g#
4) So re-write #F_W =F_C# as
#F_W = m*g =1/(4*pi*epsilon_0)*(q_1*q_2)/(r^2) = F_C #
5) #(q_1*q_2)= m*g*(4*pi*epsilon_0)*(r^2)#
6) Since #q_1=q_2#, we can write #q_1^2= m*g*(4*pi*epsilon_0)*(r^2)#
#q_1^2=50kg*9.81m/s^2*(4*3.1415*8.854 * 10^-12F/m)*(10m)^2#
#q_1^2=sqrt(5.45xx10^-6C^2)#
#q_1=2.33xx10^-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_W# is a simple, way to express this mathematically, where #F_C# represents the force between the charges and #F_W# is the weight of the person.
2) #F_C# is the (electrostatic) force acting between two charges separated by a distance #r#, where the magnitude of one of the charges is, #q_1# and the magnitude of the other charge is #q_2#. #epsilon_0# is the electric permeability of free space.
3) #F_W=m*g# tells us that the weight of the person [or any object for that matter] is the mass of the object, #m#, 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_2#, by multiplying both sides by #4*pi*epsilon_0*r^2#.
6) The phrase “Two Equal charges” indicates that we can set #q_2 = q_1#. In other words, the magnitude of each charge is the same. So #q_1*q_2=q_1^2#. After that, it’s just a matter of substituting the values for the quantities (# m,g,pi,epsilon_0 and r# ), carrying out a little arithmetic and we’re done!
