Two charges of # -4 C # and # -2 C# are positioned on a line at points # -1 # and # 4 #, respectively. What is the net force on a charge of # -4 C# at # 1 #?

Question

Two charges of #  -4  C # and #  -2 C# are positioned on a line at points # -1 # and # 4   #, respectively.  What is the net force on a charge of #  -4  C# at #  1   #?

Emily Abbate · Accepted Answer

#F_"net"=28.10^9" N"#

#F=k*(q_1*q_2)/r^2#

#r:"distance between two charges"#
#q_1:"the first charge"#
#q_2:"the second charge"#
#F_"AB":" represents the force between charges A and B"#
#F_"CB":"represents the force between charges C and B"#
#F_"AB" and F_"CB" " are opposite forces"#
#F_"AB"=k*((-4)*(-4))/2^2" "F_"AB"=(16*k)/4=4*k#

#F_"CB"=k*((-2)*(-4))/3^2=" "F_"AB"=(8k)/9#

#F_"net"=F_"AB"-F_"CB"#

#F_"net"=4*k-(8*k)/9#

#F_"net"=(36*k-8*k)/9#

#F_"net"=(28*k)/9" "k=9*10^9 #

#F_"net"=(28*cancel(9)*10^9)/cancel(9)#

#F_"net"=28.10^9" N"#

Julia Aguilar · Answer

undefined The net force on a charge of -4 C at 1 can be calculated using Coulomb's law, which states:

$$ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} $$

Where:
- $ F $ is the force between the charges,
- $ k $ is Coulomb's constant ($8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2$),
- $ q_1 $ and $ q_2 $ are the magnitudes of the charges,
- $ r $ is the distance between the charges.

Calculate the force between the charge of -4 C at 1 and the charge of -2 C at 4 using Coulomb's law. Then, since both charges are negative, the force will be attractive and directed towards the -2 C charge.