Question

In a rectangular coordinate system a charge of 25 x 10

-9C is placed at

the origin of coordinates, and a charge of 25 x 10

-9C is placed at a point

x=6 cm, y=0. What is the electric field at (a) x=3m, y=0m (b) x=3m, y=4m?​

Answer 1

Given:

In a rectangular coordinate system a charge of 25 x 10-9C is placed at the origin of coordinates, and a charge of 25 x 10-9C is placed at a point x=6 cm, y=0.

To find:

What is the electric field at (a) x=3m, y=0m (b) x=3m, y=4m?​

Solution:

We use the formula,

E = 1/4π∈₀ q/{r₀ - r}³ (r₀ - r)

The electric field at (a) x=3m, y=0m

r₀ = 6i

r = 3i

r₀ - r = 6i - 3i = 3i

E = 1/4π∈₀ q/{r₀ - r}³ (r₀ - r)

= (9 × 10^9) (25 × 10^{-9})/|√3²|³ (3i)

= (9 × 25)/27 (3i)

∴ E = 25i N/C

The electric field at (b) x=3m, y=4m

r₀ = 6i

r = 3i + 4j

r₀ - r = 6i - 3i - 4j = 3i - 4j

E = 1/4π∈₀ q/{r₀ - r}³ (r₀ - r)

= (9 × 10^9) (25 × 10^{-9})/|√(3² + 4²)|³ (3i - 4j)

= (9 × 25)/125 (3i - 4j)

∴ E = (5.4i - 7.2j) N/C