A cube of side ‘a’ has point charges +Q located at each of its vertices except at the origin where the charge is -Q. The electric field at the centre of cube is:
If charge (-Q) at origin is replaced by (+Q), then electric field at the centre of the cube is zero. Thus, electric field at the centre of the cube is as if only (-2Q) charge is present at the origin.
<p>If charge (-Q) at origin is replaced by (+Q), then electric field at the centre of the cube is zero. Thus, electric field at the centre of the cube is as if only (-2Q) charge is present at the origin.</p><p><span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>E</mi> <mo>→</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> <mfrac> <mrow> <mrow> <mo> (</mo> <mrow> <mo>−</mo> <mn>2</mn> <mi>Q</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>.</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mrow> <mo> (</mo> <mrow> <mover accent="true"> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>−</mo> <mn>2</mn> <mi>Q</mi> </mrow> <mrow> <mn>3</mn> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mi>π</mi> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mrow> <mo> (</mo> <mrow> <mover accent="true"> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span><br><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1817021053"> </o:OLEObject></xml><! [endif]-></p>
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