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https://texercises.com/exercise/potential-in-triangle/
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Exercise:
A negative qaO and a positive qbO po charge are placed at two corners of an equilateral triangle with sides aO long. Calculate the potential difference between the third corner and the midpo of the triangle.

Solution:
The distance of the third corner C to each charge is equal to the side a of the equilateral triangle. The potential at C can therefore be written as phi_C phi_-a + phi_+a k_C fracq_Aa + k_C fracq_Ba frack_Ca q_A + q_B The distance r_M between a corner and the midpo of the triangle corresponds to two thirds of the height h: r_M frac h frac fracsqrt a fracsqrt a The potential at the midpo is therefore phi_M phi_-r_M + phi_+r_M frack_Cr_M q_A + q_B fracsqrt k_Ca q_A + q_B For the potential difference we find that Delta phi phi_C - phi_M k_Cq_A+q_Bleftfraca-fracsqrt aright VF nckctimesfrac-sqrtqa+qba resultVP
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Exercise:
A negative qaO and a positive qbO po charge are placed at two corners of an equilateral triangle with sides aO long. Calculate the potential difference between the third corner and the midpo of the triangle.

Solution:
The distance of the third corner C to each charge is equal to the side a of the equilateral triangle. The potential at C can therefore be written as phi_C phi_-a + phi_+a k_C fracq_Aa + k_C fracq_Ba frack_Ca q_A + q_B The distance r_M between a corner and the midpo of the triangle corresponds to two thirds of the height h: r_M frac h frac fracsqrt a fracsqrt a The potential at the midpo is therefore phi_M phi_-r_M + phi_+r_M frack_Cr_M q_A + q_B fracsqrt k_Ca q_A + q_B For the potential difference we find that Delta phi phi_C - phi_M k_Cq_A+q_Bleftfraca-fracsqrt aright VF nckctimesfrac-sqrtqa+qba resultVP
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Electrostatics
Tags
electric potential, electric potential difference, electrostatics, point charge
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Difficulty
(4, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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