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A disk of radius produces a potential =84.4 mV at the center of the disk at point P, as shown. Assume that charge density varies linearly with the radius according to =, where =7.55×10−10 C/m3.

Calculate the radius of the disk in centimeters.

Respuesta :

okpalawalter8

We have that  the radius of the disk in centimeters.

[tex]R=6.3cm[/tex]

From the question we are told

  • A disk of radius produces a potential =84.4 mV
  • Assume that charge density varies linearly with the radius according to =, where =7.55×10−10 C/m3.

Generally the equation for Potential energy at disk center   is mathematically given as

[tex]Ve=\int^{H}_0 \frac{2\pi rdr}{r}\\\\Ve=2Ak\pi \int^{H}_0 rdr\\\\Ve=Ak\piR^2[/tex]

Therefore

[tex]R=\frac{Ve}{Ak\pi}\\\\R=\frac{84.4*10^{-3}}{7.55*10^{-10*8.99*10^9\pi}}\\\\R=6.3*10^{-2}m[/tex]

Therefore the radius of the disk in centimeters.

[tex]R=6.3*10^{-2}m[/tex]

[tex]R=6.3cm[/tex]

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