 Physics Help Forum Question about relationship between Acceleration and Electric Potential
 User Name Remember Me? Password

 Advanced Electricity and Magnetism Advanced Electricity and Magnetism Physics Help Forum Sep 29th 2019, 09:21 AM #1 Junior Member   Join Date: Sep 2019 Posts: 1 Question about relationship between Acceleration and Electric Potential Hi everyone. Im a Engineering student and i having doubts about this question: "What is the acceleration vector $\displaystyle a(x,y,z)$ of a particle of mass $\displaystyle m0$ and charge $\displaystyle q0$ when there is a Potential vector$\displaystyle V(x,y,z) = c0 x3 c1 + x-5 y5 z4$ where '$\displaystyle c0$' and '$\displaystyle c1$' are constants." Well I started with the relation $\displaystyle V = -W/q0$ (1) and $\displaystyle W = F  d$ (being F and d vectors) (2) also $\displaystyle F = m0*a$ (being 'a' a vector) (3) So I ended up with this equation that relates a and V replacing equation (3) in (2): $\displaystyle W = (m0*a)  d$(4) And replacing (4) in (1) I have: $\displaystyle V = - m0*a*d / q0$(5) Which means: $\displaystyle a = - V*q0 / m0*d$ (6) Here I got stuck and don't know how to proceed. I appreciate very much any help.   Sep 30th 2019, 05:59 AM #2 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 474 There's no need to introduce work done here. The potential is related to the electric field strength by: $\displaystyle \vec{E} = - \nabla V$ Assuming the scalar field $\displaystyle V(x,y,z) = c_0 c_1 x^3 + x - 25 yz^4$, we can compute the gradient, $\displaystyle \nabla V$. $\displaystyle \nabla V = \frac{\partial V}{\partial x} \hat{x} + \frac{\partial V}{\partial y} \hat{y} + \frac{\partial V}{\partial z} \hat{z}$ $\displaystyle = \left(3 c_0 c_1 x^2 +1\right) \hat{x} - 25z^4 \hat{y} - 100 y z^3 \hat{z}$ Assuming that the only force in the problem is the electric force, we have $\displaystyle \vec{F} = \vec{E} q_0 = m_0 \vec{a}$. Therefore, $\displaystyle \vec{a} = \frac{\vec{E} q_0}{m_0} = \frac{-q_0 \nabla V }{m_0}$ $\displaystyle = \frac{q_0}{m_0} \left(-\left(3 c_0 c_1 x^2 +1\right) \hat{x} + 25z^4 \hat{y} + 100 y z^3 \hat{z}\right)$ You might want to double-check that the potential you wrote down is the same as the one I assumed... topsquark likes this.  Tags acceleration, electric, potential, question, relationship Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post jjones6171 Thermodynamics and Fluid Mechanics 1 Feb 5th 2019 01:55 AM Punch Electricity and Magnetism 1 Jul 22nd 2011 09:33 AM jasonlewiz Electricity and Magnetism 0 Jul 23rd 2010 10:19 PM cerberus Electricity and Magnetism 4 Aug 24th 2009 12:16 PM Rainy2Day Advanced Electricity and Magnetism 0 Feb 9th 2009 03:10 PM 