Draw the orientation of electric dipole moment in a electric field such that the dipole expiriances 76.6% of the maximum torque
Answers
ᴄᴏɴsɪᴅᴇʀ ᴀ ᴅɪᴘᴏʟᴇ ᴡɪᴛʜ ᴄʜᴀʀɢᴇs +ϙ ᴀɴᴅ –ϙ ᴡɪᴛʜ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴅ ᴀᴡᴀʏ ғʀᴏᴍ ᴇᴀᴄʜ ᴏᴛʜᴇʀ. ᴛʜᴇ ᴅɪᴘᴏʟᴇ ɪs ᴘʟᴀᴄᴇᴅ ɪɴ ᴀ ᴜɴɪғᴏʀᴍ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴇ sᴜᴄʜ ᴛʜᴀᴛ ᴛʜᴇ ᴀxɪs ᴏғ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ғᴏʀᴍs ᴀɴ ᴀɴɢʟᴇ θ ᴡɪᴛʜ ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ.
ᴛʜᴇ ғᴏʀᴄᴇ ᴏɴ ᴛʜᴇ ᴄʜᴀʀɢᴇs ɪs
ғ
+
=+ϙ
ᴇ
ғ
−
=−ϙ
ᴇ
ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛs ᴏғ ғᴏʀᴄᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴀʀᴇ:
ғ
+
⊥
=+ϙᴇsɪɴθ
ғ
−
⊥
=−ϙᴇsɪɴθ
sɪɴᴄᴇ ᴛʜᴇ ғᴏʀᴄᴇ ᴍᴀɢɴɪᴛᴜᴅᴇs ᴀʀᴇ ᴇϙᴜᴀʟ ᴀɴᴅ ᴀʀᴇ sᴇᴘᴀʀᴀᴛᴇᴅ ʙʏ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴅ, ᴛʜᴇ ᴛᴏʀϙᴜᴇ ᴏɴ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ɪs ɢɪᴠᴇɴ ʙʏ:
ᴛᴏʀϙᴜᴇ(τ)=ғᴏʀᴄᴇ×ᴅɪsᴛᴀɴᴄᴇ
τ=(ϙᴇ)ᴅsɪɴθ
ɴᴏᴡ, ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴍᴏᴍᴇɴᴛ ɪs ɢɪᴠᴇɴ ʙʏ
ᴘ=ϙᴅ
ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴍᴏᴍᴇɴᴛ ɪs ғʀᴏᴍ ᴛʜᴇ ᴘᴏsɪᴛɪᴠᴇ ᴛᴏ ᴛʜᴇ ɴᴇɢᴀᴛɪᴠᴇ ᴄʜᴀʀɢᴇ. ɴᴏᴛɪᴄᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴛᴏʀϙᴜᴇ ɪs ɪɴ ᴛʜᴇ ᴄʟᴏᴄᴋᴡɪsᴇ ᴅɪʀᴇᴄᴛɪᴏɴ (ʜᴇɴᴄᴇ ɴᴇɢᴀᴛɪᴠᴇ) ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ғɪɢᴜʀᴇ ɪғ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴘᴏsɪᴛɪᴠᴇ.
ᴛʜᴜs, τ=ᴘᴇsɪɴθ
τ=
ᴘ
×
ᴇ