A hemispherical surface with radius r in a region of uniform electric field E→ has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.

Video transcript

Hey, everyone today, we're dealing with the problem about flux. Now, we're being told that a curve lending is placed in a uniform electric field. E it's a uniform electric field. The radius of a flat circular area on the left of the lenses are the optical lens axis is parallel to the fuel's direction shown as shown in the image below. With this were being asked to find out the electrical flux through the curved surface. Now, while this may seem a little complicated, it's actually really quite easy to understand. So electrical flux, electrical flux can be expressed as the man through the electric field multiplied by the area through which the field is passing through. Now, the flux passes through a flat circle, the left part of this lens, right, which means the area of that circle will simply be E in two pi R squared. Now, so this is the area entering the curved or the flux entering the circular surface. However, every electric fuel line that passes through the flat side of the circle must also pass through the curved surface of the lens as shown here below. So the flux of the curved part of the lens will be the same as the flux of the flat. So flux curved must equal flux passing through the flat side, which means the flux is simply E pi R squared. The flux through the curved surface is e multiplied by pi R squared or answer choice. See, I hope this helps and I look forward to seeing you all in the next one.