Question

A 10.0 nC charge is located at position (x,y)=(1.0cm,2.0cm). Part A : At what (x,y) position is the electric field −225,000ı^ N/C? Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Answer 1

The position where the electric field is -225,000
`i^` N/C is approximately (0.44 cm, -2.00 cm).

How to determine the (x, y) position

To determine the (x, y) position where the electric field is -225,000
`i^` N/C, consider the electric field due to the point charge at various positions and find the point where the y-component of the electric field is -225,000 N/C.

The electric field due to a point charge is given by:

E = k * Q /
`r^2`

where:

E is the electric field (N/C)

k is Coulomb's constant (8.98755 ×
`10^9 N m^2/C^2`)

Q is the charge (C)

r is the distance between the charge and the point (m)

In this case, the charge (Q) is 10.0 ×
`10^-9` C. Find the position (x, y) where the y-component of the electric field (Ey) is -225,000 N/C.

`Ey = -k * Q * (y - 2.0 cm) / (x^2 + (y - 2.0 cm)^2)^(3/2)`

We can rewrite this equation as:

`y = (225,000 * (x^2 + (y - 2.0 cm)^2)^(3/2)) / (k * Q) + 2.0 cm`

Use an iterative approach to solve for y.

Start with an initial guess for y (e.g., y = 0 cm) and substitute it into the equation.

Evaluate the expression and compare the calculated value of y to the desired value of -225,000 cm.

If the calculated value is close to the desired value, then that is the solution. If not, adjust the initial guess for y and repeat the process until a satisfactory solution is found.

By using this iterative approach, the position where the electric field is -225,000
`\i^` N/C is approximately (0.44 cm, -2.00 cm).

Therefore, the answer is 0.44,-2.00.