Question

An electric field E=10xi exists in a certain
region of space. Then the potential difference
V = V-V, where V, is the potential at the
origin and V is the potential at x=2 m is:
(a) 10
(b) - 20
(c) +20 J
(d) -10​

Answer 1

Answer:c)+20J

Explanation:

Answer 2

Concept:

An electric field is a physical field that surrounds electrically charged particles and acts as an attractor or repellent to all other charged particles in the vicinity.

Given:

The electric field is defined as $E=10x\hat{i}$.

The potential difference $V=V_0-V_A$ between the potential at origin and potential at $x=2m$.

Find:

The potential difference V.

Solution:

The relation between the electric field and potential gradient is given by:

$E=-\frac{dv}{dx}$

Therefore,

$10x=-\frac{dv}{dx}$

$10x\text{dx}=-\text{dv}$

Integrating both sides,

$\int10x\text{dx}=-\int\text{dv}$

The potential difference is calculated between the origin $x=0$ and at $x=2$.

$\int10x\text{dx}=-\int\text{dv}$

$[\frac{10x^2}{2}]=-[V_A-V_0]$

$\frac{10(2)^2}{2}-\frac{10(0)^2}{2} =V_0-V_A$

$V_0-V_A=20$

The potential difference $V$ is $+20V$.

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