Question 6: Units , Dimensions and Error Analysis

Question

An electric field $E=3 x^2 i N C^{-1}$ exists in a certain region of space. The potential difference between the origin and at $x=4 m, V_0-V_4$ is

Accepted Answer

We use the relation
$$V(b)-V(a) \;=\; -\int_{a}^{b}E\cdot dl\,. $$
Here $E_x=3x^2$, so
$\displaystyle \int_0^4E_x\,dx = \int_0^4 3x^2\,dx = 3\cdot\frac{x^3}{3}\Big|_0^4 = 64$.
Thus
$      V(4)-V(0) = -64      \quad\Longrightarrow\quad      V(0)-V(4) = +64	ext{ V.}    $
Answer: 64 V (Option D).

Answer

$-$20 V

Answer

$-$40 V

Answer

$-$64 V

Answer

64 V

Units , Dimensions and Error Analysis

An electric field E=3 x^2 i N C^{-1} exists in a certain region of space. The potential difference between the origin and at x=4 m, V_0-V_4 is

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