Problem 13.30

จาก \(\vec{E} = \vec{E}_{2} + \vec{E}_{3} + \vec{E}_{4}\)

îîĵĵ

\(\vec{E} =\frac{k(2q)}{\ell ^{2}}+\frac{k(3q)}{( 2\ell )^{2}}(\frac{1}{2}+\frac{1}{2}) +\frac{k(4q)}{\ell ^{2}}\)

îĵ

\(\vec{E} = (\frac{2kq}{\ell ^{2}}+\frac{3 2kq}{4\ell ^{2}}) + (\frac{4kq}{\ell ^{2}}+\frac{3 2kq}{4\ell ^{2}})\)

îĵ

\(\vec{E} = ((2 +\frac{3 2}{4}) + (4 +\frac{3 2}{4}) )\frac{kq}{\ell ^{2}}\)

îĵ

\(\vec{E} = (3.06 + 5.06 )\frac{kq}{\ell ^{2}}\;\blacksquare\)

จาก \(\vec{F} = q\vec{E}\)

îĵ

\(\vec{F} = q((3.06 + 5.06 )\frac{kq}{\ell ^{2}})\)

îĵ

\(\vec{F} = (3.06 + 5.06 )\frac{kq^{2}}{\ell ^{2}}\;\blacksquare\)