Question

The figure below shows three point charges, all positive. If the net electric force on the center charge is zero, what is the value of x/y?​

Answer 1

Explanation:

We know that electric field due to point charge q at distance r from it is

$e\: \: = \frac{kq}{ {r}^{2} }$

and force F = qE ( proportional to E )

Since net force is zero i.e. net electric field is zero

so 2q and 3q charge electric field must cancel out each other and their magnitude are equal

$\frac{k(2q)}{ {x}^{2} } = \frac{k(3q)}{ {y}^{2} } \\ \\ \frac{ {y}^{2} }{ {x}^{2} } = \frac{3}{2} \\ \\ \frac{y}{x} = \sqrt{ \frac{3}{2} }$

There is some misprint in options because ratio of two distance y and x can't be multiple of y .

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

The figure below shows three point charges , all positive . If the net electric force on the center charge is zero , what is the value of y/x ?

• A. $\displaystyle \frac{4}{9}$

• B. $\displaystyle \sqrt{ \frac{2}{3} }$

• C. $\displaystyle \sqrt{ \frac{3}{2} }$ ✔️

• D. $\displaystyle \frac{3}{2}$

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

As net electric force on q is zero . So , the electric force on q due to 2q is equal to electric force on q due to 3q . Therefore ,

$\displaystyle \sf \longrightarrow \frac{kq(2q)}{ {( x)}^{2} } = \frac{kq(3q)}{ {( y)}^{2} } \: \\ \\ \\ \displaystyle \sf \longrightarrow \frac{ \cancel{kq}(2q)}{ {( x)}^{2} } = \frac{\cancel{kq}(3q)}{ {( y)}^{2} } \: \\ \\ \\ \displaystyle \sf \longrightarrow \frac{2q}{ {x}^{2} } = \frac{3q}{ {y}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \displaystyle \sf \longrightarrow \frac{ {y}^{2} }{ {x}^{2} } = \frac{3q}{2q} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \displaystyle \sf \longrightarrow { \bigg (\frac{y}{x} \bigg) }^{2} = \frac{3 \cancel{q}}{2 \cancel{q}}\: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \displaystyle \sf \longrightarrow { \bigg (\frac{y}{x} \bigg) }^{2} = \frac{3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \displaystyle \sf \longrightarrow \frac{y}{x} = \sqrt{ \frac{3}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$