- #1

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1. A ring of radius [tex]a[/tex] carries a uniforly distributed positive total charge [tex]Q[/tex]. Calculate the electrical field due to the ring at a point [tex]P[/tex] lying a distance [tex]x[/tex] from its center along the central axis perpendicular to the plane of the ring.

[tex]dE_x=dEcos \theta = (k \frac{dq}{r^2})\frac {x}{r} = \frac{kx}{(x^2+a^2)^{3/2}} dq[/tex]

[tex]E_x= \int \frac{kx}{(x^2+a^2)^{3/2}}dq=\frac{kx}{(x^2+a^2)^{3/2}} \int dq[/tex]

[tex]E_x= \frac{kx}{(x^2+a^2)^{3/2}}Q [/tex]

2. A disk of radius [tex]R[/tex] has a uniform surface charge density [tex]\sigma[/tex]. Calculate the electrical field at a point [tex]P[/tex] that lies along the central perpendicular axis of the disk and a distance [tex]x[/tex] from the center of the disk.

[tex]dq=2 \pi \sigma r dr[/tex]

[tex]dE=\frac{kx}{(x^2+a^2)^{3/2}}(2 \pi \sigma r dr)[/tex]

[tex]E=kx \pi \sigma \int_0 ^R \frac{2r dr}{(x^2+a^2)^{3/2}}[/tex]

My question is:

In problem #1 vs Problem #2, why are there limits on #2 and why does #1 only integrate the dq?