Find the length of the distance r_1 from the 5 nC charge at x = -1 to the point

Question

Find the length of the distance r_1 from the 5 nC charge at x = -1 to the point P. Use the Pythagorean theorem or the distance formula, whichever you feel more comfortable with. Find the length of the distance r_2 from the 5 nC charge at x = 2 to the point P. Use the Pythagorean theorem or the distance formula. Find the contribution V_1 to the electric potential at P from the 5 nC charge at x = -1 Find the contribution V_2 to the electric potential at P from the 5 nC charge at x = 2. Find the total electric potential V = V_1 + V_2. Find the magnitude and direction of the electric field contribution E_1 at point P caused by just the charge at x = -1. (In other words, find what the electric field at P would be if the 5 nC charge at x = -1 were the only charge present.)

Explanation / Answer

As coordinates of point p are not given. let coordinates of point p to be(x,y).

1.) r1=((x+1)2+y2)1/2

2.) r2=((x-2)2+y2)1/2

3.)V1=Kq/r1=(9×109)×(5× 10-9)/((x+1)2+y2)1/2

4.)V2=Kq/r=(9×109)×(5× 10-9)/((x-2)2+y2)1/2

5.)V1+V2=[(9×109)×(5× 10-9)/((x+1)2+y2)1/2]+[(9×109)×(5× 10-9)/((x-2)2+y2)1/2]

6.)Electric field at point p=E1=ke(q/r2)rˆ=[(9×109)×(5× 10-9)/{((x+1)2+y2)1/2}2]rˆ

rˆ=((x+1)iˆ+yjˆ)

=tan-1(ry/rx)=y/x+1

magnitude of electric field at p=[(9×109)×(5× 10-9)/{((x+1)2+y2)1/2}2]

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