Question

What is the electric field (given as a vector) at coordinates (x,y,z) = (1m,2m,2m) produced by a point charge of 4 μC sitting at the origin.

Answer 1

Answer:

$\vec{E} = 1.334\hat{i} + 2.668\hat{j} + 2.668\hat{k}$ N/C

Solution:

Charge, Q = $4\mu C = 4\times 10^{- 6} C$

Coordinates (x, y, z) are (1, 2, 2)

Now, we know that the Electric field at any point in the Cartesian plane is given by:

$\vec{E} = \frac{1}{4\pi epsilon_{o}}\times \frac{Q}{|d|^{2}}\hat{d}$      (1)

where

$\frac{1}{4\pi epsilon_{o}} = 9\times 10^{9} N-m^{2}/C^{2}$

d = distance of the charge from the point

$\hat{d} = \hat{i} + 2\hat{j} + 2\hat{k}$

$|d| = \sqrt{1^{2} + 2^{2} + 2^{2}$

Now, from eqn (1):

$\vec{E} = 9\times 10^{9}\times \frac{4\times 10^{- 6}}{(\sqrt{1^{2} + 2^{2} + 2^{2})^{2}}}\times (\hat{i} + 2\hat{j} + 2\hat{k})$

$\vec{E} = 1.334(\hat{i} + 2\hat{j} + 2\hat{k})$ N/C

$\vec{E} = 1.334\hat{i} + 2.668\hat{j} + 2.668\hat{k}$ N/C