E 1 = k q 1 r 1 2 = 9 ⋅ 1 0 9 ⋅ 3 ⋅ 1 0 − 3 0. 1 2 = 2.7 ⋅ 1 0 9 V / m E_1=k\frac{q_1}{r_1^2}=9\cdot10^9\cdot \frac{3\cdot10^{-3}}{0.1^2}=2.7\cdot10^9V/m E 1 = k r 1 2 q 1 = 9 ⋅ 1 0 9 ⋅ 0. 1 2 3 ⋅ 1 0 − 3 = 2.7 ⋅ 1 0 9 V / m
E 2 = k q 2 r 2 2 = 9 ⋅ 1 0 9 ⋅ 5 ⋅ 1 0 − 3 0. 1 2 = 4.5 ⋅ 1 0 9 V / m E_2=k\frac{q_2}{r_2^2}=9\cdot10^9\cdot \frac{5\cdot10^{-3}}{0.1^2}=4.5\cdot10^9V/m E 2 = k r 2 2 q 2 = 9 ⋅ 1 0 9 ⋅ 0. 1 2 5 ⋅ 1 0 − 3 = 4.5 ⋅ 1 0 9 V / m
E 3 = k q 3 r 3 2 = 9 ⋅ 1 0 9 ⋅ 5 ⋅ 1 0 − 3 ( 0.1 2 ) 2 = 2.25 ⋅ 1 0 9 V / m E_3=k\frac{q_3}{r_3^2}=9\cdot10^9\cdot \frac{5\cdot10^{-3}}{(0.1\sqrt{2})^2}=2.25\cdot10^9V/m E 3 = k r 3 2 q 3 = 9 ⋅ 1 0 9 ⋅ ( 0.1 2 ) 2 5 ⋅ 1 0 − 3 = 2.25 ⋅ 1 0 9 V / m
E x = E 3 cos 45 ° + E 2 = ( 2.25 cos 45 ° + 4.5 ) ⋅ 1 0 9 = 6.1 ⋅ 1 0 9 V / m E_x=E_3\cos45°+E_2=(2.25\cos45°+4.5)\cdot10^9=6.1\cdot10^9V/m E x = E 3 cos 45° + E 2 = ( 2.25 cos 45° + 4.5 ) ⋅ 1 0 9 = 6.1 ⋅ 1 0 9 V / m
E y = − E 3 sin 45 ° + E 1 = ( − 2.25 sin 45 ° + 2.7 ) ⋅ 1 0 9 = 1.1 ⋅ 1 0 9 V / m E_y=-E_3\sin45°+E_1=(-2.25\sin45°+2.7)\cdot10^9=1.1\cdot10^9V/m E y = − E 3 sin 45° + E 1 = ( − 2.25 sin 45° + 2.7 ) ⋅ 1 0 9 = 1.1 ⋅ 1 0 9 V / m
E = E x 2 + E y 2 = 1 0 9 ⋅ 6. 1 2 + 1. 1 2 = 6.2 ⋅ 1 0 9 V / m E=\sqrt{E_x^2+E_y^2}=10^9\cdot\sqrt{6.1^2+1.1^2}=6.2\cdot10^9V/m E = E x 2 + E y 2 = 1 0 9 ⋅ 6. 1 2 + 1. 1 2 = 6.2 ⋅ 1 0 9 V / m
Comments
Leave a comment