Answer:
electric potential, V = -q(a²- b²)/8π∈₀r³
Explanation:
Question (in proper order)
Consider two thin coaxial, coplanar, uniformly charged rings with radii a and b (b < a) and charges q and -q, respectively. Determine the potential at large distances from the rings
<em>consider the attached diagram below</em>
the electric potential at point p, distance r from the center of the outer charged ring with radius a is as given below
Va = q/4π∈₀ [1/(a² + b²)¹/²]
Also
the electric potential at point p, distance r from the center of the inner charged ring with radius b is
Sum of the potential at point p is
V = Va + Vb
that is
the expression below can be written as the equivalent
likewise,
hence,
1/r is common to both equation
hence, we have it out and joined to the 4π∈₀ denominator that is outside
by reciprocal rule
1/a² = a⁻²
by binomial expansion of fractional powers
where
if we expand the expression we have the equivalent as shown
also,
the above equation becomes
Answer
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