COMEDK · Physics · 17. Electrostatics
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
- A \(-20 \mathrm{~V}\)
- B 64 V
- C \(-64 \mathrm{~V}\)
- D \(-40 \mathrm{~V}\)
Answer & Solution
Correct Answer
(B) 64 V
Step-by-step Solution
Detailed explanation
The relationship between electric field \(\vec{E}\) and electric potential \(V\) is given by \(dV = -\vec{E} \cdot d\vec{r}\). Given \(\vec{E} = 3x^2 \hat{i}\), we have \(dV = -3x^2 dx\). To find the potential difference \(V_0 - V_4\), we integrate from \(x=4\) to \(x=0\):…
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