Question

A uniform field of 2.0 NC−1 exists in space in the x-direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z). (b) At which point, the potential is 25 V? (c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at a general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?

Answer 1

Answer:

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Answer 2

(a)  v = -2x

(b)  x = – 12.5 m  

(c) 100 – 2x  

(d)Potential at origin is ∞

Taking the potential at infinity to be zero is not practical, because in that case, we have to take the potential at source to be infinity and the calculations will become practically impossible.

Explanation:

Given

E = 2 N/C in x - direction

(a)

Potential a at the origin is O.

$d V=-E_{x} d x-E_{y} d y-E_{z} d z$

$\begin{aligned}&v-0=-2 x\\&\mathrm{v}=-2 \mathrm{x}\end{aligned}$

(b)

(25 – 0) = – 2x  

x = – 12.5 m  

(c)

If potential at origin is 100 v,  

v – 100 = – 2x  

V = – 2x + 100 = 100 – 2x  

(d)

Potential at ∞ is 0,

V – V' = – 2x

V' = V + 2x = 0 + 2∞  

V' = ∞  

Potential at origin is ∞

Taking the potential at infinity to be zero is not practical, because in that case, we have to take the potential at source to be infinity and the calculations will become practically impossible.