al-difference-vab-vb-va-for-motion-from-radius-a-to-radius-b-along-a-radial-path

Question

In a region where the electric field is radial and given by E(r)=αr2E(r)=\frac{\alpha}{$$r^2$$} directed outward, what is the potential difference VAB=V(B)−V(A)V_{AB}=V(B)-V(A) for motion from radius AA to radius BB along a radial path, where A"\u003eB\u003eAB\u003eA?

Accepted Answer

α(1B−1A)\alpha(\frac{1}{B}-\frac{1}{A})

Answer

α(B−A)α(B - A)

Answer

α(1A−1B)\alpha(\frac{1}{A}-\frac{1}{B})

Answer

αln⁡(BA)\alpha\ln(\frac{B}{A})

In a region where the electric field is radial and given by E(r)=αr2E(r)=\(\frac{\alpha}{r^2}\) directed outward, what is the potential difference VAB=V(B)−V(A)V_{AB}=V(B)-V(A) for motion from radius AA to radius BB along a radial path, where B>AB>A?

In a region where the electric field is radial and given by $E (r) = \frac{α}{r^{2}}$ directed outward, what is the potential difference $V_{A B} = V (B) - V (A)$ for motion from radius $A$ to radius $B$ along a radial path, where $B > A$ ?