Two point charges are 10.0 cm apart and have charges of 2.0 #muC# and -2.0 #muC#, respectively. What is the magnitude of the electric field at the midpoint between the two charges?

• Every electric charge has a electric field.
• The charges in the electric field are affected each other.
• As you move away from the electric charge, the intensity of the electric field decreases.
• The electric field is a vector quantity.
• The electric field of each charge is calculated to find the intensity of the electric field at a point.
• The vectorial sum of the vectors are found.
• The electric field of the positive charge is directed outward from the charge.

• the electric field of the negative charge is directed towards the charge.

• we can draw this pattern for your problem.

#"let the electric field of charge +2 "mu C" be " color(red)(E_1)" (red vector)"#

#d=5 cm=5.10^(-2)m#
#q_1=+2 mu C=+2*10^(-6)C#

• The electric field of a charge is calculated by formula :

#E=k.(q)/(d^2)#

#color(red)(E_1=k*(2.10^(-6))/(5.10^(-2))=+k*0.4*10^(-4)N/C)#

#color(blue)(E_2=k*(-2.10^(-6))/(5.10^(-2))=-k*0.4*10^(-4)N/C)#

• The electric field of the charges at the point C is #E_C#

#E_C=color(red)(E_1)+color(blue)(E_2)#

#E_C=k*0.4*10^(-4)+k*0.4*10^(-4)#

#E=2*k*0.4*10^(-4)=0.8*k*10^(-4)#

#k=9.10^9#

#E_C=0.8*9.10^9*10^(-4)#

#E_C=7.2*10^5 N/C#