Question

prove that elwctric field is conservative

Answer 1

we proved that an electric field is a conservative field, because, curl of electric field is zero or, say, the line integral of electric field is path independent or, say, the closed line integral of electric field is zero. Due to this fact we can associate a potential function with electric field.
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Answer 2

Hello dear................


ᴡᴇ ᴘʀᴏᴠᴇᴅ ᴛʜᴀᴛ ᴀɴ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴀ ᴄᴏɴsᴇʀᴠᴀᴛɪᴠᴇ ғɪᴇʟᴅ, ʙᴇᴄᴀᴜsᴇ, ᴄᴜʀʟ ᴏғ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴢᴇʀᴏ ᴏʀ, sᴀʏ, ᴛʜᴇ ʟɪɴᴇ ɪɴᴛᴇɢʀᴀʟ ᴏғ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴘᴀᴛʜ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴏʀ, sᴀʏ, ᴛʜᴇ ᴄʟᴏsᴇᴅ ʟɪɴᴇ ɪɴᴛᴇɢʀᴀʟ ᴏғ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴢᴇʀᴏ.

ᴅᴜᴇ ᴛᴏ ᴛʜɪs ғᴀᴄᴛ ᴡᴇ ᴄᴀɴ ᴀssᴏᴄɪᴀᴛᴇ ᴀ ᴘᴏᴛᴇɴᴛɪᴀʟ ғᴜɴᴄᴛɪᴏɴ ᴡɪᴛʜ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ.