Question

Two point charges of2micro c and 8 micro c are placed 12 cm apart. Find the point where electric field intensity is zero

Answer 1

Answer:

• The Electric Field intensity will be zero at 4 cm (From 2 μC)

Given:

1. Given Charges:- 2 μC & 8 μC
2. Distance of separation (d) = 12 cm

Explanation:

$\rule{300}{1.5}$

For Figure Kindly see the attachment !

Since, Both the given charges are of same sign i.e. Positive the null point will lie in between the charges.

Let, Point "P" be the point where the electric field is zero.

For electric field to be zero, the electric field of both the charges will be equal. Let the neutral point be x from 2 μC and (12 - x) from 8 μC.

Now, Equating both the Electric fields,

$\displaystyle\Rightarrow\bf{E_{\;(2\;\mu\;C)}=E_{\;(8\;\mu\;C)}}\\\\\\\Rightarrow\sf \dfrac{K\;Q_{1}}{(d_{1})^{2}}=\dfrac{K\;Q_{2}}{(d_{2})^{2}}$

Substituting the values,

• d₁ = x meters.
• d₂ = (12 - x) meters.

$\displaystyle\Rightarrow\sf \dfrac{K\times 2\;\mu\;C}{(x)^{2}}=\dfrac{K\times 8\;\mu\;C}{(12 - x)^{2}}\\\\\\\Rightarrow\sf \dfrac{K\times 2\times 10^{-6}}{(x)^{2}}=\dfrac{K\times 8\times 10^{-6}}{(12 - x)^{2}}$

Since,

• 1 μ C = 10⁻⁶ C

$\Rightarrow\sf \dfrac{2\times 10^{-6}}{(x)^{2}}=\dfrac{8\times 10^{-6}}{(12 - x)^{2}}\\\\\\\Rightarrow\sf \dfrac{2}{(x)^{2}}=\dfrac{8}{(12 - x)^{2}}\\\\\\\Rightarrow\sf \dfrac{1}{(x)^{2}}=\dfrac{4}{(12-x)^{2}}$

Taking square root on both sides,

$\displaystyle\Rightarrow\sf \sqrt{\dfrac{1}{(x)^{2}}}=\sqrt{\dfrac{4}{(12-x)^{2}}}\\\\\\\Rightarrow\sf \dfrac{1}{x}=\dfrac{2}{(12-x)}\\\\\\\Rightarrow\sf 1\times (12-x)=2\times x\\\\\\\Rightarrow\sf 12 - x = 2 \;x\\\\\\\Rightarrow\sf 2\;x=12-x\\\\\\\Rightarrow\sf 2\;x+x=12\\\\\\\Rightarrow\sf 3\;x=12\\\\\\\Rightarrow\sf x=\dfrac{12}{3}$

$\displaystyle\Rightarrow\sf x=4\\\\\\\Rightarrow\large{\underline{\boxed{\red{\sf x=4\;cm}}}}$

∴ The Electric Field intensity will be zero at 4 cm (From 2 μC).

$\rule{300}{1.5}$

Answer 2

$\huge\underline\mathbb\purple{Answer:-}$

The Electric Field intensity will be zero at 4 cm (From 2 μC)