Answered: 12µc 30cm -13uc -13µC 97 9. --9uc

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12µc 30cm -13uc -13µC 97 9. --9uc

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Question

a) Find the total electric force exerted by the charges in the hexagon on the charge at the center

b) Determine the magnitude of the electric field in the center of the hexagon

91 = 9uc
92 12µc
30cm
96 =13µc
e-13µc
97
95 =12µc

Expert Solution

Step 1

Given: The charge $q_{1}$ is $- 9 μC$ .

The charge $q_{2}$ is $12 μC$ .

The charge $q_{3}$ is $- 13 μC$ .

The charge $q_{4}$ is $- 9 μC$ .

The charge $q_{5}$ is $12 μC$ .

The charge $q_{6}$ is $13 μC$ .

The charge $q_{7}$ is $- 9 μC$ .

The distance between any of the two charges is 30 cm.

To determine: (a) Total electric force exerted by all the charges on the charge at center.

Like charges repel each other and unlike charges attract each other.

The force between the two charges is given as

$F = \frac{1}{4 π ε_{0}} \frac{q Q}{r^{2}}$

where F is the force between the two charges, $q and Q$ are the two charges and r is the distance between the two charges.

The direction of force due to charge $q_{1}$ on $q_{7}$ is repulsive, it will along the charge $q_{4}$ . Similarly the direction of force due to charge $q_{4}$ on $q_{7}$ is repulsive and will be along $q_{1}$ . These two forces will cancel out each other.