$Q_{enc}$

Electricity and Magnetism Level 3

Given a closed surface $S$ there is always an outward pointing normal, where by outward pointing we mean that if I travel along the normal direction I can keep going forever without intersecting $S$ again. We can use a similar definition of inside and outside of $S$ . $Q_{enc}$ on the right hand side of Gauss' law is simply the total charge inside $S$ .

We have a line of alternating charges on the $x$ -axis at $x=...,-2,-1,0,1,2,....$ with a positive charge at the origin. What is the total charge inside a sphere of radius $3.5$ , i.e. what is $Q_{enc}$ ?

The answer is -1.

1 solution

Soumya Dubey
Mar 2, 2015

Considering that the sphere is centered at origin with radius 3.5 .so in the positive direction of x-axis i get a total -ve charge of -2units and +ve charge of 1 unit.Repeating the same in -ve direction of x -axis i get total charge enclosed by the surface =-1 units

$Q_{enc}$

The answer is -1.

1 solution

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Q e n c Q_{enc} Q e n c ​

The answer is -1.

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$Q_{enc}$