A Charged particle of mass 1.0 g is suspended through a
. silk thread of length 40 cm in a horizantal electric field
. of `4.0 xx 10 ^4 NC ^(-1)` . If the particle stays aty a distance of
. 24 cm from the wall in equilibrium, find the charge on
. the particle.

Explanation

To solve the problem step by step, we will analyze the forces acting on the charged particle suspended by a silk thread in a horizontal electric field.

### Step 1: Understanding the Setup
We have a charged particle of mass \( m = 1.0 \, \text{g} = 1.0 \times 10^{-3} \, \text{kg} \) suspended by a silk thread of length \( L = 40 \, \text{cm} = 0.4 \, \text{m} \). The particle is in a horizontal electric field \( E = 4.0 \times 10^{4} \, \text{N/C} \) and is at a distance of \( d = 24 \, \text{cm} = 0.24 \, \text{m} \) from the wall.

### Step 2: Finding the Angle \( \theta \)
The horizontal distance from the wall to the particle is \( d = 0.24 \, \text{m} \), and the length of the thread is \( L = 0.4 \, \text{m} \). We can find the vertical distance \( h \) from the wall to the particle using the Pythagorean theorem:

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