Question

Any answer with steps will be appreciated... Thank you so much..

Three charged insulating wires, all of length 0.5 m, are connected together to form the object shown. Find the magnitude of the electric field at the geometric center of the object, given that qı = 7 nC, q2 = -3 nC, and q3 = -4 nC. The charge on each wire is distributed uniformly. 92

Answer 1

the expression for the electric field at a point P on the perpendicular bisector of a uniformly charged rod or wire of length L and having a charge Q, point P is at a distance 'a' from the rod

Date T feld atepoint far the Ron te prpeadicular The exprtssion electic bisecor 6t unifocmy harged od, t lungta , haviy dislance Pis a charge D, and rods at a 'a trem the 2 2 S49 4 T Fo Tu

The expression for the electric field is given in the figure above

Y-axis E2 6 >Xaxir C, E3

The direction of the respective electric fields is given in the figure above

Let O be the center of the object and L be the length of each wire

Then according to the geometry of the equilateral triangle

The perpendicular distance of the point O from each wire will be = L/2(3)^1/2

Hence this will be the value of a in the expression for electric field

Putting this value in the electric field expression we get

E = 6kQ/L², k is the constant

E₁ = 6kq₁/L²(cos(30)i - sin(30)j)

E₂ = 6kq₂/L²(cos(30)i + sin(30)j)

E₃ = 6kq₃/L²(-j)

Adding all three electric field and calculating the magnitude of the net electric field = 778.8 N/C