Five charges are arranged as shown in the figure; four identical charges form a square of side d while a fifth charge Q of mass m is suspended above the center of the square, a height d above its plane. (a) What is the charge Q if the charge is in equilibrium? (b) What type of equilibrium does the charge enjoy?

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Five charges are arranged as shown in the figure; four identical charges
form a square of side d while a fifth charge Q of mass m is suspended
above the center of the square, a height d above its plane. (a) What
is the charge Q if the charge is in equilibrium? (b) What type of
equilibrium does the charge enjoy?
Transcribed Image Text:Five charges are arranged as shown in the figure; four identical charges form a square of side d while a fifth charge Q of mass m is suspended above the center of the square, a height d above its plane. (a) What is the charge Q if the charge is in equilibrium? (b) What type of equilibrium does the charge enjoy?
Expert Solution
Step 1

For charge Q to be in equilibrium net forces on Q should be 0.

FnetQ=0FnetQx=0FnetQy=0

Net force in x direction on Q

FQx=0Fq1Qcos 45°+Fq2Qcos 45°-Fq3Qcos 45°-Fq4Qcos 45°=0Fq1Q+Fq2Qcos 45°=Fq3Q+Fq4Qcos45°Fq1Q+Fq2Q=Fq1Q+Fq2Q

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