Consider a point charge qqq in three-dimensional space. Symmetry requires the electric field to point directly away from the charge in all directions. To find E(r)E(r)E(r), the magnitude of the field at distance rrr from the charge, the logical Gaussian surface is a sphere centered at the charge. The electric field is normal to this surface, so the dot product of the electric field and an infinitesimal surface element involves cos(0)=1cos⁡(0)=1. The flux integral is therefore reduced to ∫E(r)dA=E(r)A(r)∫E(r)dA=E(r)A(r), where E(r)E(r)E(r) is the magnitude of the electric field on the Gaussian surface, and A(r)A(r)A(r) is the area of the surface.

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.