Three point charges are placed at the vertices of a right-angled triangle in the…

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Three point charges are placed at the vertices of a right-angled triangle in the

xy

-plane:

A(0,0)

carries

+5\,\mu\text{C}

B(0,0.06\,\text{m})

carries

-3\,\mu\text{C}

, and

C(0.08\,\text{m},0)

carries

+2\,\mu\text{C}

. (i) Write an expression for the total electric potential

V(x,y)

at an arbitrary point

P(x,y)

in the plane due to the three charges. (ii) By setting

V(x,y)=0

, derive the simultaneous algebraic equations that the coordinates of a zero-potential point

P

must satisfy. (iii) Solve these equations to find the coordinates of a point in the first quadrant

(x>0,\,y>0)

where the electric potential is zero. (iv) Comment on the uniqueness of this point within the plane for the given charge configuration. (Take

\dfrac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}