Distinguish difference between electric potential and electric potential energy
Electric Potential $(V)$ | Electric Potential Energy $(U)$ |
$(1)$ Work done against electric field to bring unit positive charge is electric potential. | $(1)$ Work done against electric field to bring charge ' $q$ ' is electric potential energy |
$(2)$ Unit : $JC$ $^{-1}$ or Volt. | $(2)$ Unit : $J$ (Joule) |
$(3)$ $\mathrm{V}=\frac{\mathrm{W}}{q}, q=$ unit positive charge. | $(3)$ $\mathrm{U}=q \mathrm{~V}$ |
$(4)$ $[\mathrm{V}]=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-1}$ | $(4)$ $[\mathrm{U}]=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$ |
$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \;\mu C$ and $-2\; \mu C$ (and with no external field) placed at $(-9 \;cm , 0,0)$ and $(9\; cm , 0,0)$ respectively.
$(b)$ How much work is required to separate the two charges infinitely away from each other?
$(c)$ Suppose that the same system of charges is now placed in an external electric field $E=A\left(1 / r^{2}\right) ; A=9 \times 10^{5} \;C m ^{-2} .$ What would the electrostatic energy of the configuration be?
A point charge $q$ is surrounded by eight identical charges at distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?
A pellet carrying a charge of $0.5$ coulomb is accelerated through a potential of $2000$ volts. It attains some kinetic energy equal to
$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7}\; C$ located $9 \;cm$ away.
$(b)$ Hence obtain the work done in bringing a charge of $2 \times 10^{-9} \;C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?
A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]