Problem 20.50 (Figure 1) shows five electric charges. Four charges with the magn

Question

Problem 20.50

(Figure 1) shows five electric charges. Four charges with the magnitude of the charge 2.0 nC form a square with the size a = 3.0 cm . Positive charge with the magnitude of q = 1.0 nC is placed in the center of the square.

Part A

What is the magnitude of the force on the 1.0 nC charge in the middle of the figure due to the four other charges?

Express your answer to two significant figures and include the appropriate units.

g

Part B

What is the direction of the force on the 1.0 nC charge in the middle of the figure due to the four other charges?

Could you please explain each step so I can better understand. Thank you!

Figure 1 of 1

Problem 20.50

(Figure 1) shows five electric charges. Four charges with the magnitude of the charge 2.0 nC form a square with the size a = 3.0 cm . Positive charge with the magnitude of q = 1.0 nC is placed in the center of the square.

Part A

What is the magnitude of the force on the 1.0 nC charge in the middle of the figure due to the four other charges?

Express your answer to two significant figures and include the appropriate units.

g

Part B

What is the direction of the force on the 1.0 nC charge in the middle of the figure due to the four other charges?

=   , counterclockwise from the positive x-axis

Could you please explain each step so I can better understand. Thank you!

Figure 1 of 1

2.0 nC 2.0 nC 2.0 nC 2.0 nC

Explanation / Answer

electric force = F= kq1q2/r^2

distance between 1 nC and 2 nC = sqrt(2)*(3/2) = 2.12 cm = 2.12*10^(-2) m

magnitude of charge 2 nC on charge q=1 nC = 9*10^9*2*10^(-6)*1*10^(-6)/( 2.12*10^(-2))^2 = 40.05 N

net force on q due to both +ve 2nC charges = sqrt(40.05^2 + 40.05^2) = 56.63 N

direction is along -ve x-axis.

net force on q due to both -ve 2nC charges = sqrt(40.05^2 + 40.05^2) = 56.63 N

direction is along -ve x-axis.

net electric force on q due to all foure 2 nC = 56.63 + 56.63 = 113.26 N

and direction is along -ve x-axis means 180 degree counterclock wise from +x axis.

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