Respuesta :
Answer:
(a) 6650246.305 N/C
(b) 24150268.34 N/C
(c) 6408227.848 N/C
(d) 665024.6305 N/C
Explanation:
Given:
Radius of the ring (r) = 10.0 cm = 0.10 m [1 cm = 0.01 m]
Total charge of the ring (Q) = 75.0 μC = [tex]75\times 10^{-6}\ \mu C[/tex] [1 μC = 10⁻⁶ C]
Electric field on the axis of the ring of radius 'r' at a distance of 'x' from the center of the ring is given as:
[tex]E_x=\dfrac{kQx}{(x^2+r^2)^\frac{3}{2}}[/tex]
Plug in the given values for each point and solve.
(a)
Given:
[tex]Q=75\times 10^{-6}\ \mu C[/tex], [tex]r=0.01\ m, a=1.00\ cm=0.01\ m,k=9\times 10^{9}\ Nm^2/C^2[/tex]
Electric field is given as:
[tex]E_x=\dfrac{(9\times 10^{9})(75\times 10^{-6})(0.01)}{((0.01)^2+(0.1)^2)^\frac{3}{2}}\\\\E_x=\dfrac{6750}{1.015\times 10^{-3}}\\\\E_x=6650246. 305\ N/C[/tex]
(b)
Given:
[tex]Q=75\times 10^{-6}\ \mu C[/tex], [tex]r=0.01\ m, a=5.00\ cm=0.05\ m,k=9\times 10^{9}\ Nm^2/C^2[/tex]
Electric field is given as:
[tex]E_x=\dfrac{(9\times 10^{9})(75\times 10^{-6})(0.05)}{((0.05)^2+(0.1)^2)^\frac{3}{2}}\\\\E_x=\dfrac{33750}{1.3975\times 10^{-3}}\\\\E_x=24150268.34\ N/C[/tex]
(c)
Given:
[tex]Q=75\times 10^{-6}\ \mu C[/tex], [tex]r=0.01\ m, a=30.0\ cm=0.30\ m,k=9\times 10^{9}\ Nm^2/C^2[/tex]
Electric field is given as:
[tex]E_x=\dfrac{(9\times 10^{9})(75\times 10^{-6})(0.30)}{((0.30)^2+(0.1)^2)^\frac{3}{2}}\\\\E_x=\dfrac{202500}{0.0316}\\\\E_x=6408227.848\ N/C[/tex]
(d)
Given:
[tex]Q=75\times 10^{-6}\ \mu C[/tex], [tex]r=0.01\ m, a=100\ cm=1\ m,k=9\times 10^{9}\ Nm^2/C^2[/tex]
Electric field is given as:
[tex]E_x=\dfrac{(9\times 10^{9})(75\times 10^{-6})(1)}{((1)^2+(0.1)^2)^\frac{3}{2}}\\\\E_x=\dfrac{675000}{1.015}\\\\E_x=665024.6305\ N/C[/tex]
