Answer:
A) B = 0.009185 T
B) Drection is negative y-direction
Explanation:
A) We are given;
Speed(v) = 2.5 x 10^(7) m/s
Acceleration (a) = 2.2 x 10^(13) m/s²
We also know that charge of proton(q) = 1.6 x 10^(-19)
Mass of proton(m) = 1.67 x 10^(-27)
Now, Since the proton is moving by circular motion, this force is equal to the centripetal force which is given as;
F = qvBsinθ = ma
Since perpendicular, θ = 90°
And so, sinθ = sin 90 = 1
Thus, qvB = ma
Making B the subject gives;
B = ma/qv
B = (1.67 X 10^(-27) X 2.2 X 10^13)) / (1.6 X 10^(-19) X 2.5 X 10^(7))
= 0.009185 T
B) By use of Flemings right hand rule, we can see that the middle finger points toward negative y-direction, so the magnetic field is in the negative y-direction
602.496 J I think, I hope this helps!
<span>1. Plasma membrane - also known as cell membrane. It is 'the skin of a cell', which acts as a physically controlling barrier for the entrance and exit of materials. It's made up of proteins and lipids.
2. Cytoplasm - everything inside the cell (but not including the nucleus). Much of the cytoplasm is a transparent and gel-like material known as cytosol; cell structures are suspended in it.
3. Ribosomes - these are organelles that are in charge of making proteins.
<span>4. DNA - Molecules containing the genetic code of a cell, which tells the cell what to do. It is located in the nucleus for eukaryotic cells; for prokaryotic cells, it is located in a part of the cell called the nucleoid.</span></span>
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>
