$A$ non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times 10^{-10}\,C$ distributed non-uniformly on its circumference,producing an electric field $\vec{E}$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} { - \vec{E} \cdot d\vec{l} }$ (where $l = 0$ is the centre of the ring) in volts is:

  • A
    $2$
  • B
    $-1$
  • C
    $-2$
  • D
    $0$

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Similar Questions

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero,no matter which path is chosen.
Reason $R :$ Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements,choose the correct answer from the options given below.

$90 \ J$ of work is done to move an electric charge of magnitude $3 \ C$ from a place $A$,where potential is $-10 \ V$,to another place $B$,where potential is $V_1 \ V$. The value of $V_1$ is: (in $V$)

$A$ hollow charged metal sphere has radius $R$. If the potential difference between its surface and a point at a distance $5R$ from the centre is $V$,then the magnitude of the electric field intensity at a distance $5R$ from the centre of the sphere is:

$A$ hollow metal sphere of radius $15 \,cm$ is charged such that the potential on its surface is $20 \,V$. Then, the potential at the centre of the sphere is (in $V$)

$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

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