Physics

Problem

A point charge of

-9.0\,\mu\text{C}

is located at point

A

in the

x

–

y

plane. Points

P

and

Q

lie on a straight line that makes an angle of

45^{\circ}

with the positive

x

-axis, at distances

0.50\,\text{m}

and

1.00\,\text{m}

, respectively, from

A

. Take

k = 9.0\times10^{9}\,\text{N m}^2\text{C}^{-2}

. a. (i) Calculate the electric-field vector at point

P

in component form

(E_x,\,E_y)

. b. (ii) Calculate the electric-field vector at point

Q

in component form

(E_x,\,E_y)

. c. (iii) Find the vector difference

\Delta \mathbf{E} = \mathbf{E}_P - \mathbf{E}_Q

. Show algebraically that the magnitude of

\Delta \mathbf{E}

is proportional to

\left(\dfrac{1}{r_1^{2}} - \dfrac{1}{r_2^{2}}\right)

, where

r_1

and

r_2

are the distances

0.50\,\text{m}

and

1.00\,\text{m}

, respectively. Evaluate the numerical value of

|\Delta \mathbf{E}|