Kinetic energy because it is moving
Answer:
Explanation:
Plate separation, d = 1.76 cm = 0.0176 m
Area of plates, A = 25 cm^2 = 0.0025 m^2
V = 255 V
(a) Capacitance of capacitor
C = 1.258 x 10^-12 F
charge is same before and after immersion as the battery is disconnected
q = C V
q = 1.258 x 10^-12 x 255 = 3.2 x 10^-10 C
(b)
Capacitance before, C = 1.258 x 10^-12 C
capacitance after, C' = k x C = 80 x 1.258 x 10^-12 = 100.64 x 10^-12 C
Where, k is the dielectric constant of water = 80
Potential difference after immersion, V' = V / k = 255 / 80 = 3.1875 V
(c) initial energy,
Final energy
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:
Explanation:
We shall apply conservation of momentum along x and y axis.
Let the final momentum of second particle be p₁ along x axis and p₂ along y axis.
Considering momentum along x axis
2 + 0 = 3 cos 45 + p₁
p₁ = 2-2.12 = - 0.12 kg m/s
Considering momentum along y axis
4 + 0 = 3 sin 45 + p₂
p₂ = 4-2.12 = 1.88 kg m/s
Final momentum = √ ( p₁² + p₂² )
=√ ( .12² + 1.88² )
= 1.88 approx
The answer to your question is kidneys
