Question

charge of 10 micro coulomb, -10 micro coulomb, 15 micro coulomb and 30 micro coulomb
are placed in order of cat each of the corners
of a square of 10 cm side & calculate
the potential at the point of Interpection
of diogonals​

Answer 1

Given:

charge of 10 micro coulomb, -10 micro coulomb, 15 micro coulomb and 30 micro coulomb

are placed in order on the corners

of a square of 10 cm.

To find:

Net potential at the intersection of diagonals.

Calculation:

Net potential

$= \dfrac{k(q1)}{d} + \dfrac{k(q2)}{ d } + \dfrac{k(q3)}{d} + \dfrac{k(q4)}{d}$

$= \dfrac{k}{d} \bigg \{(q1) + (q2) + (q3) + (q4) \bigg \}$

$= \dfrac{k}{d} \bigg \{(10 - 10 + 15 + 30) \times {10}^{ - 6} \bigg \}$

$= \dfrac{k}{d} \bigg \{( 45) \times {10}^{ - 6} \bigg \}$

$= \dfrac{k}{d} \bigg \{ 45 \times {10}^{ - 6} \bigg \}$

$= \dfrac{9 \times {10}^{9} }{d} \bigg \{ 45 \times {10}^{ - 6} \bigg \}$

$= \dfrac{9 \times {10}^{9} }{ (\frac{0.1}{ \sqrt{2} }) } \bigg \{ 45 \times {10}^{ - 6} \bigg \}$

$= \dfrac{9 \times {10}^{10} }{ (\frac{1}{ \sqrt{2} }) } \bigg \{ 45 \times {10}^{ - 6} \bigg \}$

$= 9 \sqrt{2} \times {10}^{10} \bigg \{ 45 \times {10}^{ - 6} \bigg \}$

$= 405 \sqrt{2} \times {10}^{ 4}$

$= 4.05 \sqrt{2} \times {10}^{ 6} \: volt$

So , final answer is:

$\boxed{ \sf{ \red{potential = 4.05 \sqrt{2} \times {10}^{ 6} \: volt}}}$