a) \(\overrightarrow {{E_M}} = \overrightarrow {{E_1}} + \overrightarrow {{E_2}} \)
Ta có: \(\left\{ \begin{array}{l}{E_1} = k\dfrac{{\left| {{q_1}} \right|}}{{A{M^2}}} = {9.10^9}\dfrac{{\left| {{{4.10}^{ - 8}}} \right|}}{{0,{1^2}}} = 0,{36.10^5}\left( {V/m} \right)\\{E_2} = k\dfrac{{\left| {{q_2}} \right|}}{{B{M^2}}} = {9.10^9}\dfrac{{\left| { - {{4.10}^{ - 8}}} \right|}}{{0,{1^2}}} = 0,{36.10^5}\left( {V/m} \right)\end{array} \right.\)
Lại có \(\overrightarrow {{E_1}} \uparrow \uparrow \overrightarrow {{E_2}} \)
\( \Rightarrow {E_M} = {E_1} + {E_2} = 0,{36.10^5} + 0,{36.10^5} = 0,{72.10^5}V/m\)
b) \(\overrightarrow {{E_N}} = \overrightarrow {{E_1}} + \overrightarrow {{E_2}} \)
Ta có: \(\left\{ \begin{array}{l}{E_1} = k\dfrac{{\left| {{q_1}} \right|}}{{A{N^2}}} = {9.10^9}\dfrac{{\left| {{{4.10}^{ - 8}}} \right|}}{{0,{1^2}}} = 0,{36.10^5}\left( {V/m} \right)\\{E_2} = k\dfrac{{\left| {{q_2}} \right|}}{{B{N^2}}} = {9.10^9}\dfrac{{\left| { - {{4.10}^{ - 8}}} \right|}}{{0,{3^2}}} = 0,{04.10^5}\left( {V/m} \right)\end{array} \right.\)
Lại có \(\overrightarrow {{E_1}} \uparrow \downarrow \overrightarrow {{E_2}} \)
\( \Rightarrow {E_N} = {E_1} - {E_2} = 0,{36.10^5} - 0,{04.10^5} = 0,{32.10^5}V/m\)
c) Ta có: \(\left\{ \begin{array}{l}AI = 16cm\\BI = 12cm\\AB = 20cm\end{array} \right.\)
\(A{I^2} + B{I^2} = A{B^2}\)
\( \Rightarrow \Delta ABI\) vuông tại I
\(\overrightarrow {{E_I}} = \overrightarrow {{E_1}} + \overrightarrow {{E_2}} \)
Ta có: \(\left\{ \begin{array}{l}{E_1} = k\dfrac{{\left| {{q_1}} \right|}}{{A{I^2}}} = {9.10^9}\dfrac{{\left| {{{4.10}^{ - 8}}} \right|}}{{0,{{12}^2}}} = 0,{25.10^5}\left( {V/m} \right)\\{E_2} = k\dfrac{{\left| {{q_2}} \right|}}{{B{I^2}}} = {9.10^9}\dfrac{{\left| { - {{4.10}^{ - 8}}} \right|}}{{0,{{16}^2}}} = 0,{14.10^5}\left( {V/m} \right)\end{array} \right.\)
Lại có \(\overrightarrow {{E_1}} \bot \overrightarrow {{E_2}} \)
\( \Rightarrow {E_I} = \sqrt {E_1^2 + E_2^2} = \sqrt {\left( {0,{{25.10}^5}} \right) + {{\left( {0,{{14.10}^5}} \right)}^2}} = 0,{287.10^5}V/m\)
