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The axial field is the integration of the field from each element of charge around the ring. Because of symmetry, the field is only in the direction of the axis. The field from an element ds in the ring is
<span>dE = (qs*ds)cos(T)/(4*pi*e0)*(x^2 + R^2) </span>
<span>where x is the distance along the axis from the plane of the ring, R is the radius of the ring, qs is the linear charge density, T is the angle of the field from the x-axis. </span>
<span>However, cos(T) = x/sqrt(x^2 + R^2) </span>
<span>so the equation becomes </span>
<span>dE = (qs*ds)*[x/sqrt(x^2 + R^2)]/(4*pi*e0)*(x^2 + R^2) </span>
<span>dE =[qs*ds/(4*pi*e0)]*x/(x^2 + R^2)^1.5 </span>
<span>Integrating around the ring you get </span>
<span>E = (2*pi*R/4*pi*e0)*x/(x^2 + R^2)^1.5 </span>
<span>E = (R/2*e0)*x*(x^2 + R^2)^-1.5 </span>
<span>we differentiate wrt x, the term R/2*e0 is a constant K, and the derivative is </span>
<span>dE/dx = K*{(x^2 + R^2)^-1.5 +x*[(-1.5)*(x^2 + R^2)^-2.5]*2x} </span>
<span>dE/dx = K*{(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5} </span>
<span>to find the maxima set this = 0, giving </span>
<span>(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5 = 0 </span>
<span>mult both side by (x^2 + R^2)^2.5 to get </span>
<span>(x^2 + R^2) - 3*x^2 = 0 </span>
<span>-2*x^2 + R^2 = 0 </span>
<span>-2*x^2 = -R^2 </span>
<span>x = (+/-)R/sqrt(2) </span>
Answer:
1,1 m
Explanation:
Dado que;
coeficiente de fricción = 0,6
sabemos que W = R = mgcos 37 = 3.5Kg * 10m / s ^ 2 * cos37 = 27.95 N
coeficiente de fricción = fuerza / reacción normal (R)
Fuerza = 0.6 * 27.95 N
Fuerza (F) = 16.77 N
Recuerda que F = Ke
dónde;
K = constante de fuerza (15N / m)
e = extensión (lo desconocido)
e = F / K
e = 16,77 N / 15 N / m
e = 1,1 m
Answer:
3 : 08 : 10.9
Explanation:
assuming a 12 hour clock
angular velocity of the hour hand is 2π/(3600(12)) rad/s
angular velocity of the minute hand is 2π/3600 rad/s
difference is 2π/3600 - 2π/(3600(12)) = 11(2π/(3600(12)) rad/s
45° = π/4 radians
This angle is covered in a time of
π/4 rad / 22π / (3600(12)) = 900(12) / 22 = 490.909090... s
or about 8 minutes 10.9 s
ANSWER 3:08:10.9
Answer:
"Man's mind is far too advanced for his survival needs."
See also "Wallace", Darwin's junior partner who couldn't explain the gap in intelligence.
