Determine the charge that produces an electric field strength of 40 V/cm at a distance of 30cm in vacuum(in 10-8C)

To find the charge that produces an electric field strength (E) of 40 V/cm at a distance (r) of 30 cm in a vacuum, we can use the formula for the electric field due to a point charge:

[

E = frac{k cdot |q|}{r^2}

]

Where:

– (E) is the electric field strength (in V/m),

– (k) is Coulomb’s constant, approximately (8.99 times 10^9 , text{N m}^2/text{C}^2),

– (q) is the charge (in coulombs),

– (r) is the distance from the charge (in meters).

Step 1: Convert units

– (E = 40 , text{V/cm} = 4000 , text{V/m})

– (r = 30 , text{cm} = 0.3 , text{m})

Step 2: Rearrange the formula to solve for charge (q)

[

|q| = frac{E cdot r^2}{k}

]

Step 3: Substitute the values

[

|q| = frac{4000 , text{V/m} cdot (0.3 , text{m})^2}{8.99