If the electric potential at any point (x, y, z)m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3)m will be

<p>According to relation between field and potential, we can write</p><p><math><mrow><mover accent="true"><mi>E</mi><mo>→</mo></mover><mo>=</mo><mo>−</mo><mfrac><mrow><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mrow><mo> (</mo><mrow><mover accent="true"><mi>i</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mrow><mi>d</mi><mrow><mo> (</mo><mrow><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mrow><mo> (</mo><mrow><mover accent="true"><mi>i</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mn>6</mn><mi>x</mi><mrow><mo> (</mo><mrow><mover accent="true"><mi>i</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow></mrow></math></p><p><math><mrow><msub><mrow><mover accent="true"><mi>E</mi><mo>→</mo></mover></mrow><mrow><mrow><mo> (</mo><mrow><mn>1</mn><mo>, </mo><mtext> </mtext><mn>0</mn><mo>, </mo><mtext> </mtext><mn>3</mn></mrow><mo>)</mo></mrow></mrow></msub><mo>=</mo><mo>−</mo><mn>6</mn><mrow><mo> (</mo><mrow><mover accent="true"><mi>i</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow><mi>N</mi><mo>/</mo><mi>C</mi></mrow></math></p>

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