Please give step by step 3. A positive charge +2Q lies at x =-a, and a charge-Q
ID: 1579306 • Letter: P
Question
Please give step by step
3. A positive charge +2Q lies at x =-a, and a charge-Q lies at x-ta. (a) Derive an expression for the potential on the x - axis and find a point on the axis in the region x > a where the potential (with respect to infinity) is zero (b) Use your expression for the potential to find the (c) Is the electric field zero where the potential is zero? If not, where is a. the field zero? 4. Find the potential as a function of position in an electric field given by E = a x where a is a constant and where V = 0 at x = 0.Explanation / Answer
3. (A) V = k (2 Q) / (x - (-a)) + k (-Q)/(x - a)
{ potential due to a charge, V = k q / r }
(where k = 1 / (4 pi e0))
V = ( Q / 4 pi e0) [ 2/(x + a) - 1/(x - a)]
(B) E = - dV/dx
E =( Q / (4 pi e0)) [ 2 / (x + a)^2 - 1 / ( x - a)^2]
(C) V = 0
2x -2 a = x + a
x = 3 a
E = 0
(x + a) / (x - a) = 1.414
x + a = 1.414 x - 1.414 a
x = 5.8 a
NO,
for E = 0 => x = 5.8 a