Poblem 16E Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of -3.63 X 1016 N ? m2/C at the planet’s surface. Calculate: (a) the total electric charge on the planet; (b) the electric field at the planet’s surface (refer to the astronomical data inside the back cover); (c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet’s surface.
Solution 16E Step 1 of 4: The mars planet has magnetic field which produces the net flux 16 2 e 3.63 × 10 N.m /C at the planet’s surface. We need to calculate the Part(a) the total electric charge on the planet q= Using Gauss’s law. For part(b) by using relation between flux and electric field we can calculate the electric field at the planet’s surface E= and in part(c) we need to calculate the surface charge density on the mars = Given , 16 Electric flux, e= 3.63 × 10 N.m /C 2 Radius of mars, r=3.4 × 10 m6 Permittivity of free space, 0= 8.854 × 10 12F/m To find (a) Charge on mars, q= (b) Electric field at the planet’s surface E= (c) surface charge density on the mars = Step 2 of 4: (a) the total electric charge on the planet; Gauss’s law states that, the total electric flux through the closed surface is equal to the net charge enclosed divided by .0 That is, = q e 0 Solving for q, q = e 0 Substituting =e3.63 × 10 N.m /C , = 8.854 0 10 12F/m q = ( 3.63 × 10 N.m /C) (8.854 × 10 12F/m) 5 q = 3.21 × 10 C Therefore, the total electric charge on the mars planet is 3.21 × 10 C . 5