Question

Three equal 1.05-μC point charges are placed at the corners of an equilateral triangle whose sides are 0.300 m long. What is the potential energy of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.)

Answer 1

Potential energy of the system = 0.099 J

Step-by-step explanation:

Electrical potential energy for two charge system when zero potential energy is considered at infinitely far

`U=(1)/(4\pi\epsilon_0 ) (q_1\cdot q_2)/(r)`

`Where, q_1\ & q_2\ are\ magnitude\ of\ charge.\\and\ r\ is\ the\ distance\ between\ the\ charge.\\and\ (1)/(4\pi\epsilon_0 ) =9\cdot10^9 N m^2C^-2`

`Given, q_1=q_2 =q_3= 1.05 \cdot10^-6\ C\\and\ r=0.3\ m\\Since\ charges\ are\ placed\ at\ the\ corners\ of\ equilateral\ triangle`

`U= 3\cdot(1)/(4\pi\epsilon_0 ) (q_1\cdot q_2)/(r)= 3\cdot9\cdot10^9\cdot1.05\cdot10^-6\cdot1.05\cdot10^-6\cdot(1)/(0.3)=0.099\ J`

Hence, potential energy of the system = 0.099 J