Question

4 indentical charges each of value 2 mc are placed at the four corners of square 2 meters. What is the electric potential at the centre of the square​​​

Answer 1

`{\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}} \\ \\`

`\:\:\:\:\bullet\:\:\:\sf{ 4 \: identical \: charges = 2 \mu \: C \:\:\:(each)} \\\\`

`\:\:\:\:\bullet\:\:\:\sf{Side \: of \: square = 2 \: m }`

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`{\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}} \\ \\`

`\:\:\:\:\bullet\:\:\:\sf{ Electric \: potential \: at \: centre\:( V_(c))}`

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`{\mathfrak{\underline{\purple{\:\:\: Calculation:-\:\:\:}}}} \\ \\`

☯ According to the given data,

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`\:\:\:\:\bullet\:\:\:\sf{Length \: of \: diagonal= √(2) a } \\\\`

`\:\:\:\:\bullet\:\:\:\sf{ Length \:of \: half \: diagonal = √(2)}`

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☯ As we know that,

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`\dashrightarrow\:\: \sf{V_(c) = V_(1) + V_(2) + V_(3) + V_(4) }`

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`\sf{(V_(1) = V_( 2) = V_(3) = V_(4)) }`

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`\dashrightarrow\:\: \sf{V_(c) = 4 V_(1) }`

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`\dashrightarrow\:\: \sf{ V_(c) = 4 * (k q_(1))/( r_(1))}`

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`\dashrightarrow\:\: \sf{V_(c) = 4 * \frac{9 * {10}^(9) * 2 * {10}^( - 6) }{√(2)} }`

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`\dashrightarrow\:\: \sf{V_(c) =4 * 9 * √(2) * {10}^(9 - 6) }`

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`\dashrightarrow\:\: \sf{V_(c) =36√(2) * {10}^(3) }`

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`\dashrightarrow\:\: \underline{\boxed{\sf{V_(c) =3.6√(2) * {10}^(4) \: J /c }}}`

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★ The electric potential at center of square is 3.6
`√(2)` × 10⁴ J/c