Six equal point charges Q = 10nC are located at 2,3,4,5,6,7m. Find the potential at origin.

To find the electric potential ( V ) at the origin due to multiple point charges, we use the formula for the electric potential due to a single charge:

[

V = k frac{Q}{r}

]

where ( V ) is the electric potential, ( k ) is Coulomb’s constant (( k approx 8.99 times 10^9 , text{N m}^2/text{C}^2 )), ( Q ) is the charge, and ( r ) is the distance from the charge to the point where the potential is being calculated (in this case, the origin).

For six equal point charges each of ( Q = 10 , text{nC} = 10 times 10^{-9} , text{C} ) located at distances of 2 m, 3 m, 4 m, 5 m, 6 m, and 7 m from the origin, we calculate the potential at the origin due to each charge and then sum them up.

Calculating the potential contributions from each charge:

1. From charge at ( 2 , text{m} ):

[

V_2 = k frac{10 times 10^{-9}}{2} = 8.99 times 10^9 frac{10 times 10^{-9}}{2} = 44