Question

Calculate the electric field intensity which would be just sufficient to balance the weight of a particle of charge $-10\mu c$and mass$10mg$. [take$g=10m{s}^{-2}$].

Answer 1

Step 1: Given data:
The charge of the particle is $-10\mu c$.
Mass is $10mg$.

Gravitational acceleration g = $10m{s}^{-2}$

Step 2: Formula used:
The formula of electric intensity is
${\overrightarrow{F}}_q=q\overrightarrow{E}$.

Step 3: Find the electric field:

As the force on a charge $q$ in an electric field $\overrightarrow{E}$ is

${\overrightarrow{F}}_q=q\overrightarrow{E}$

So, according to the given problem:

Where $W$is the weight of the particle.

$\left|{\overrightarrow{F}}_q\right|=\left|\overrightarrow{W}\right|$ i.e., $\left|q\right|E=mg$

i.e., $E=\frac{mg}{\left|q\right|}$

$E=\frac{10\times {10}^{-6}\times 10}{10\times {10}^{-6}}$

$=10N/C$ in the downward direction.

The electric field is $10N/C$.