JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
Assume that an electric field \(\vec E = 30{x^2}\hat i\) exists in space. Then the potential difference \(V_A-V_O\) where \(V_O\) is the potential at the origin and \(V_A\) the potential at \(x = 2\ m\) is....\(V\)
- A \(-120\)
- B \(-80\)
- C \(80\)
- D \(120\)
Answer & Solution
Correct Answer
(B) \(-80\)
Step-by-step Solution
Detailed explanation
Potential difference between any two points in an electric field is given by, \({\mathrm{d} \mathrm{V}=-\vec{E} \cdot \overrightarrow{d x}}\) \({\int_{V_{O}}^{V_{A}} d V=-\int_{0}^{2} 30 x^{2} d x}\) \({V_{A}-V_{O}=-\left[10 x^{3}\right]_{0}^{2}=-80\, \mathrm{J} / \mathrm{C}}\)
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