Question

Two point charges of +16 μC and -9 μC are placed 8cm apart in air. Find the position of the point at which the resultant electric field is zero.

Answer 1

SoLuTioN :

➡ Given:

✏ Two point charges of +16$\mu$C and -9$\mu$C are placed 8cm apart in air.

➡ To Find:

✏ The position of the point at which the resultant electric field is zero.

➡ Formula:

✏ Formula of electric field is given by

$\underline{ \boxed{ \pink{\bold{ \sf{E = \frac{kq}{ {r}^{2} } }}}}} \: \orange{ \bigstar}$

➡ Terms indication:

✏ E denotes electric field of point charge

✏ k denotes coloumb's constant

✏ q denotes charge

✏ r denotes distance

➡ Calculation:

✏ Let distance of null point from +16$\mu$C is x cm.

✏ Therefore, distance between null point and -9$\mu$C will be (8 - x) cm.

$\implies \sf \: \frac{ \cancel{k} \times 16}{ {x}^{2} } = \frac{ \cancel{k} \times 9}{ {(8 - x)}^{2} } \\ \\ \implies \sf \: \frac{x}{8 - x} = \frac{4}{3} \\ \\ \implies \sf \: 3x + 4x = 32 \\ \\ \implies \sf \: 7x = 32 \\ \\ \star \: \boxed{ \red{ \sf{x = 4.57 \: cm}}} \: \star$

Answer 2

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

(i) The two charges i.e

• 16 μC or 16 × (10)^-6 C
• -9 μC or (10)^-6 C are located at A and B

(ii) The distance b/w A and B = 8 cm

Let ,

• P be the point where electric field is zero
• The distance b/w A and P = (x) cm
• The distance b/w P and B = (8 - x) cm

We know that , the electric field at point P will be zero if

$\mathtt{ \large{ \fbox{Electric \: field \: due \: q_{1} = Electric \: field \: due \: q_{2}}}}$

and

$\large \mathtt{ \fbox{Electric \: field = k \frac{q}{ {(r)}^{2} } }}$

Thus ,

$\sf \hookrightarrow k \frac{16 \times {(10)}^{ - 6} }{ {(x)}^{2} } = k\frac{9 \times {(10)}^{ - 6} }{ {(8 - x)}^{2} } \\ \\\sf \hookrightarrow 16 {(8 - x)}^{2} = 9 {(x)}^{2} \\ \\ \: \: \sf Taking \: square \: root \: on \: both \: sides \: \: we \: get \\ \\ \sf \hookrightarrow 4(8 - x) = 3x \\ \\ \sf \hookrightarrow 32 - 4x = 3x \\ \\\sf \hookrightarrow 32 = 7x \\ \\ \sf \hookrightarrow x = 4.57 \: \: cm$

Hence , the electric field will be zero at 4.57 cm to the right of first charge

______________ Keep Smiling ☺