Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is

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Q.
Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

1 $\frac{r}{(1 + \sqrt{3})}$

2 $\frac{(1 + \sqrt{3})}{r}$

3 $r (1 + \sqrt{3})$

4 $\frac{r}{3 (1 + \sqrt{3})}$

Ans.
(1)

${({\vec{E}}_{net})}_{P} = 0 \Rightarrow \frac{k q}{x^{2}} = \frac{k \cdot 3 q}{{(r - x)}^{2}}$

${(r - x)}^{2} = 3 x^{2}$

$r - x = \sqrt{3} x \Rightarrow x = \frac{r}{\sqrt{3} + 1}$

Solution

Q.
Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

1 $\frac{r}{(1 + \sqrt{3})}$

2 $\frac{(1 + \sqrt{3})}{r}$

3 $r (1 + \sqrt{3})$

4 $\frac{r}{3 (1 + \sqrt{3})}$

Ans.
(1)

${({\vec{E}}_{net})}_{P} = 0 \Rightarrow \frac{k q}{x^{2}} = \frac{k \cdot 3 q}{{(r - x)}^{2}}$

${(r - x)}^{2} = 3 x^{2}$

$r - x = \sqrt{3} x \Rightarrow x = \frac{r}{\sqrt{3} + 1}$

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Solution

Q. Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

1 r(1+3)

2 (1+3)r

3 r(1+3)

4 r3(1+3)

Ans. (1) (E→net)P=0⇒kqx2=k·3q(r-x)2 (r-x)2=3x2 r-x=3x⇒x=r3+1

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Q.
Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

1 $\frac{r}{(1 + \sqrt{3})}$

2 $\frac{(1 + \sqrt{3})}{r}$

3 $r (1 + \sqrt{3})$

4 $\frac{r}{3 (1 + \sqrt{3})}$

Ans.
(1)

${({\vec{E}}_{net})}_{P} = 0 \Rightarrow \frac{k q}{x^{2}} = \frac{k \cdot 3 q}{{(r - x)}^{2}}$

${(r - x)}^{2} = 3 x^{2}$

$r - x = \sqrt{3} x \Rightarrow x = \frac{r}{\sqrt{3} + 1}$