Two charges of # -7 C # and # -2 C# are positioned on a line at points # -3 # and # 6 #, respectively. What is the net force on a charge of # -8 C# at # -2 #?

Question

Two charges of #  -7  C # and #  -2 C# are positioned on a line at points # -3  # and # 6     #, respectively.  What is the net force on a charge of #  -8  C# at #  -2  #?

Charles Aeschliman · Accepted Answer

The force is #=+506.2510^9N#

The overall force is

#F=k(q_1*q_3)/r_1^2+k(q_2*q_3)/r_2^2#

The charge #q_1=-7C#

The charge #q_2=-2C#

The charge #q_3=-8C#

The distance #r_1=-2-(-3)=1m#

The distance #r_2=6-(-2)=8m#

The constant #k=9*10^9Nm^2C^-2#

Consequently,

# F= 9*10^9 (((-7) *(-8)) / 1^2 + ((-8)*(-2)) / 8^2) #

#=+910^9(56+1/4)N#

#=+506.25*10^9N#

The #+# sign indicates that the force is repulsive.

Adam Arnold · Answer

undefined To find the net force on a charge of -8 C at -2, we need to calculate the force exerted by each of the other charges individually and then sum them. The force between two charges is given by Coulomb's law, which states:

F = k * |q1 * q2| / r^2

where F is the force, k is Coulomb's constant (8.99 * 10^9 N m^2 / C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.

First, calculate the force between the charge of -8 C and the charge of -7 C at -3:

F1 = (8.99 * 10^9) * |-8 * -7| / (3)^2

Then, calculate the force between the charge of -8 C and the charge of -2 C at 6:

F2 = (8.99 * 10^9) * |-8 * -2| / (8)^2

Finally, sum the forces:

Net force = F1 + F2