Question

write and prove gauss theorem?​

Answer 1

According to Gauss's theorem the net-outward normal electric flux through any closed surface of any shape is equivalent to 1/ε0 times the total amount of charge contained within that surface.

Proof of Gauss law of electrostatics (Integral Form):

let us consider a small area element dS around a point P on the surface where the electric field produced by the charge +q is E. if E is along OP and area vector dS is along the outward drawn normal to the area element dS.

Answer 2

• ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ɢᴀᴜss's ᴛʜᴇᴏʀᴇᴍ ᴛʜᴇ ɴᴇᴛ-ᴏᴜᴛᴡᴀʀᴅ ɴᴏʀᴍᴀʟ ᴇʟᴇᴄᴛʀɪᴄ ғʟᴜx ᴛʜʀᴏᴜɢʜ ᴀɴʏ ᴄʟᴏsᴇᴅ sᴜʀғᴀᴄᴇ ᴏғ ᴀɴʏ sʜᴀᴘᴇ ɪs ᴇϙᴜɪᴠᴀʟᴇɴᴛ ᴛᴏ 1/ε0 ᴛɪᴍᴇs ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀᴍᴏᴜɴᴛ ᴏғ ᴄʜᴀʀɢᴇ ᴄᴏɴᴛᴀɪɴᴇᴅ ᴡɪᴛʜɪɴ ᴛʜᴀᴛ sᴜʀғᴀᴄᴇ.