An aluminized. spherical hot air balloon with a radius of 11m is struck by light

Question

An aluminized. spherical hot air balloon with a radius of 11m is struck by lightning. This gives the balloon a net charge of 40C. What is the electrostatic energy of the charged balloon? It is probably easiest to approach this using the capacitance of the balloon. 1.3 times 1012J 6.5 times 1011 J 3.3 times 1011 J 1.0 times 1010 J 1.6 times l010 J The figure to the right shows a finite line charge with uniform linear charge density X. The line charge occupies the y axis from 0 to L. Write the integral that you would evaluate to compute the electric potential at a point P a distance R from the line charge the x axis. Let the potential at infinity be zero. k lambda dy/ k lambda dy/ k lambda dy/ k lambda dy/ k lambda dy/ A piece of plexiglass (k = 3.2) is placed above an infinite plane of charge with charge density sigma = -0.1mu c/m2. Compute the bound charge density, row B. on the bottom surface of the dielectric. Be careful of the sign. -1.7 times 10-8 C/m2 1.7 times 10-8 C/m2 -3.4 times 10-8 C/m2 3.4 times l0-8 C/m2 -5.5 times 10-6 C/m2

Explanation / Answer

For a spherical shell,

capacitance = 4 pi e0 / [ 1/r1 - 1/r2 ]

In case charged conducting charges sphere ,

r1 - > R and r2 -> infinity

C = 4 x pi x 8.854 x 10^-12 / [ 1 /R - 0 ]

C = 4 x pi x 8.854 x 10^-12 x 11 = 1.224 x 10^-9 F

and energy stored in a capacitor = Q^2 / 2C

= 40^2 / (2 x 1.224 x 10^-9 ) = 6.53 x 10^11 J

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