Point charges $Q_1=300μ$ C located at (1, -1, -3)m experiences a force $\overline{F_1}=8 \overline{a_x }- 8 \overline{a_y }+ 4 \overline{a_z} N$ due to point charges $Q_2$ at (3, -3,-2)m. Determine $Q_2$ .

Mumbai University > Electronics Engineering > Sem 5 > Electromagnetic Engineering

Marks: 5 Marks

Year: May 2015

Given:

$Q_1=300μC at (1 ,-1,-3) \\ \overline{F_1}=8 \overline{a_x }- 8 \overline{a_y }+ 4 \overline{a_z} N \\ Q_2=? \ \ \ \ at (3,-3,-2) \\ \overline{F_1} =\dfrac{Q_1.Q_2}{4πε_o R^2} \overline{a_R} \\ \overline{a_R}=\dfrac{(1-3) \overline{a_x }+ (-1+3) \overline{a_y }+ (-3-2) \overline{a_z }}{\sqrt{2^2+ 2^2+ 5^2}} \\ \overline{a_R}=\dfrac{-2 \overline{a_x }+ 2 \overline{a_y }-5 \overline{a_z }}{\sqrt{33}} \\ 8 \overline{a_x }- 8 \overline{a_y }+ 4 \overline{a_z}=\dfrac{300 μ Q_2.(2)}{4πε_o (33)}\sqrt{33} \bigg[\dfrac{-2 \overline{a_x }+ 2 \overline{a_y }-5 \overline{a_z }}{\sqrt{33}}\bigg]$

Comparing terms of x , y and z

$8=\dfrac{300 μ Q_2.(2)}{4πε_o (33)}\sqrt{33} \\ Q_2= -281.3 μc$