I NEED HELP PLEASE, THANKS! :) Three positive charges A, B, and C, and a negative charge D are placed in a line as shown in the diagram. All four charges are of equal magnitude. The distances between A and B, B and C, and C and D are equal.
a. Which charge experiences the greatest net force? Which charge experiences the smallest net force?
b. Find the ratio of the greatest to the smallest net force.

charge C = greatest net force

charge B = the smallest net force

ratio  = 9 : 1

Explanation:

we know that in Electrostatic Forces, when 2 charges are at same sign then they repel each other and if they are different signed charges then they attract each other

so as per Coulomb's formula of Electrostatic Forces

F =     .....................1

and here k is 9 × N.m²/c² and we consider each charge at distance d

so two charge force at A to B is

F1 =

and force between charges at A to C, at 2d distance

F1 =  =  

force between charges at A to D,  3d distance

F1 =  =  

so

Charge a It receives force to the left from b and c and to the right from d

so at a will be

F(a)  = -F1 - F2 + F3             ....................2

put here value

F(a) =

solve it

F(a) =  

F(a) =   = 1.13 F1  

and

Charge b It  receives force to the right from a and d and to the left from c

F(b) = F1 - F1 + F2            ....................3

F(b)  =      

F(b)  =    =  0.25 F1

and

Charge c It receives forces to the right from all charges.

F(c) = F2 + F 1 + F 1      ....................4

F(c) =      

F(c) =     = 2.25 F1

and

Charge d It receives forces to the left from all charges

F(d) = - F3 - F2 -F 1      ....................5

F(d) =  

so

F(d) =    = 1.36 F1

and

now we get here ratio of the greatest to the smallest net force that is

ratio =

 ratio  = 9 : 1

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