# Two questions on electric potential

1. Oct 1, 2005

### stunner5000pt

Particle of mass, m, charge q>0 is projected toward a nucleus of charge +Q assumed to be at fixed postiion/
a) If the aim is perfect then how close to the center of the nucleus will the particle reach when it comes to a halt?

$$q(V_{f} - V{i}) = K$$ Vi = 0
$$q \frac{1}{4 \pi \epsilon_{0}} \frac{qQ}{r} = K$$
$$r = \frac{Qq^2}{4 \pi \epsilon_{0} K}$$

am i correct with the formula for V?

With a particular imperfect aim the particle reaches twice the distnace as above. Calculate the initial velocity.
So i imply plug r = 2r into the first answer and break K = 1/2 mv^2 and solve for v?

A charge per unit length lambda is distributed uniformly along a thin rod of length L.
a) Determine the potential at a point P at a distnace y from one end of the rod, in line with the rod.

so $$V = \frac{1}{4 \pi \epsilon_{0}} \int_{s=0}^{s=L} \frac{dq}{y+s}$$ $$dq = \lambda ds$$
and $$V = \frac{1}{4 \pi \epsilon_{0}} (\ln{y+L} - \ln{y})$$
$$V = \frac{Q}{4 \pi \epsilon_{0} L} \ln{\frac{y+L}{y}}$$
b)Use the result to determine the resulting electric field
Since the rod is thin no X or z components
$$E = \frac{\partial V}{\partial y} = \frac{Q}{4 \pi \epsilon_{0} y(y+L)}$$
am i correct?

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Last edited: Oct 1, 2005