In a certain plane, on a standard set of x-y coordinate axes, the electric poten
ID: 1520465 • Letter: I
Question
In a certain plane, on a standard set of x-y coordinate axes, the electric potential is given by V(x, y) = ax^2 + by, where V is measured in volts, and x and y are measured in meters. Calculate the work you would need to do on a proton to move it from the origin (at rest) to the point (2, 3), bringing it again to rest. Calculate the initial acceleration (both magnitude and direction) of the proton if you release it from rest at the point (2, 3). Possibly useful data: a = 0.123 V/m^2 b = -45.6 V/m e = 1.60 times 10^-19C m_p = 1.67 times 10^-27kgExplanation / Answer
Part a)
Work=Vxq
V at (2,3)=ax*2+by=0.123x4+(-45.6)x3=-136.308 V
So, work=-136.308x1.6x10^-19
W=-2.18x10^-17J
Part b)
F=m.a
F=q.E
ma=qE
a=1.6x10^-19x(136.308/5)/1.67x10^-27
a=2611889820.36 m/sec2