Brainlist question
potential energy of a dipole in an external field with proper diagram
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Answers
Explanation:
Consider a dipole with charges q1 = +q and q2 = -q placed in a uniform electric field as shown in the figure above. The charges are separated by a distance d and the magnitude of electric field is E. The force experienced by the charges is given as –qE and +qE, as can be seen in the figure.
As we know that, when a dipole is placed in a uniform electric field, both the charges as a whole do not experience any force, but it experiences a torque equal to τ which can be given as,
This torque rotates the dipole unless it is placed parallel or anti-parallel to the field. If we apply an external and opposite torque, it neutralizes the effect of this torque given by τext and it rotates the dipole from the angle Ɵ0 to an angle Ɵ1 at an infinitesimal angular speed without any angular acceleration.
The amount of work done by the external torque can be given by
As we know that the work done in bringing a system of charges from infinity to the given configuration is defined as the potential energy of the system, hence the potential energy U(Ɵ) can be associated to the inclination Ɵ of the dipole using the above relation.
From the above equation, we can see that the potential energy of dipole placed in an external field is zero when the angle Ɵ is equal to 90° or when the dipole makes an angle of 90°.
Considering the initial angle to be the angle at which the potential energy is zero, the potential energy of the system can be given as,
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Brainlist question
potential energy of a dipole in an external field with proper diagram
Try to solve in copy for brainlist
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ᴄᴏɴsɪᴅᴇʀ ᴀ ᴅɪᴘᴏʟᴇ ᴡɪᴛʜ ᴄʜᴀʀɢᴇs ϙ1 = +ϙ ᴀɴᴅ ϙ2 = -ϙ ᴘʟᴀᴄᴇᴅ ɪɴ ᴀ ᴜɴɪғᴏʀᴍ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴀs sʜᴏᴡɴ ɪɴ ᴛʜᴇ ғɪɢᴜʀᴇ ᴀʙᴏᴠᴇ. ᴛʜᴇ ᴄʜᴀʀɢᴇs ᴀʀᴇ sᴇᴘᴀʀᴀᴛᴇᴅ ʙʏ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴅ ᴀɴᴅ ᴛʜᴇ ᴍᴀɢɴɪᴛᴜᴅᴇ ᴏғ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ɪs ᴇ. ᴛʜᴇ ғᴏʀᴄᴇ ᴇxᴘᴇʀɪᴇɴᴄᴇᴅ ʙʏ ᴛʜᴇ ᴄʜᴀʀɢᴇs ɪs ɢɪᴠᴇɴ ᴀs –ϙᴇ ᴀɴᴅ +ϙᴇ, ᴀs ᴄᴀɴ ʙᴇ sᴇᴇɴ ɪɴ ᴛʜᴇ ғɪɢᴜʀᴇ.
ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ, ᴡʜᴇɴ ᴀ ᴅɪᴘᴏʟᴇ ɪs ᴘʟᴀᴄᴇᴅ ɪɴ ᴀ ᴜɴɪғᴏʀᴍ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ, ʙᴏᴛʜ ᴛʜᴇ ᴄʜᴀʀɢᴇs ᴀs ᴀ ᴡʜᴏʟᴇ ᴅᴏ ɴᴏᴛ ᴇxᴘᴇʀɪᴇɴᴄᴇ ᴀɴʏ ғᴏʀᴄᴇ, ʙᴜᴛ ɪᴛ ᴇxᴘᴇʀɪᴇɴᴄᴇs ᴀ ᴛᴏʀϙᴜᴇ ᴇϙᴜᴀʟ ᴛᴏ τ ᴡʜɪᴄʜ ᴄᴀɴ ʙᴇ ɢɪᴠᴇɴ ᴀs,
ᴛʜɪs ᴛᴏʀϙᴜᴇ ʀᴏᴛᴀᴛᴇs ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴜɴʟᴇss ɪᴛ ɪs ᴘʟᴀᴄᴇᴅ ᴘᴀʀᴀʟʟᴇʟ ᴏʀ ᴀɴᴛɪ-ᴘᴀʀᴀʟʟᴇʟ ᴛᴏ ᴛʜᴇ ғɪᴇʟᴅ. ɪғ ᴡᴇ ᴀᴘᴘʟʏ ᴀɴ ᴇxᴛᴇʀɴᴀʟ ᴀɴᴅ ᴏᴘᴘᴏsɪᴛᴇ ᴛᴏʀϙᴜᴇ, ɪᴛ ɴᴇᴜᴛʀᴀʟɪᴢᴇs ᴛʜᴇ ᴇғғᴇᴄᴛ ᴏғ ᴛʜɪs ᴛᴏʀϙᴜᴇ ɢɪᴠᴇɴ ʙʏ τᴇxᴛ ᴀɴᴅ ɪᴛ ʀᴏᴛᴀᴛᴇs ᴛʜᴇ ᴅɪᴘᴏʟᴇ ғʀᴏᴍ ᴛʜᴇ ᴀɴɢʟᴇ Ɵ0 ᴛᴏ ᴀɴ ᴀɴɢʟᴇ Ɵ1 ᴀᴛ ᴀɴ ɪɴғɪɴɪᴛᴇsɪᴍᴀʟ ᴀɴɢᴜʟᴀʀ sᴘᴇᴇᴅ ᴡɪᴛʜᴏᴜᴛ ᴀɴʏ ᴀɴɢᴜʟᴀʀ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ.
ᴛʜᴇ ᴀᴍᴏᴜɴᴛ ᴏғ ᴡᴏʀᴋ ᴅᴏɴᴇ ʙʏ ᴛʜᴇ ᴇxᴛᴇʀɴᴀʟ ᴛᴏʀϙᴜᴇ ᴄᴀɴ ʙᴇ ɢɪᴠᴇɴ ʙʏ
ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴛʜᴇ ᴡᴏʀᴋ ᴅᴏɴᴇ ɪɴ ʙʀɪɴɢɪɴɢ ᴀ sʏsᴛᴇᴍ ᴏғ ᴄʜᴀʀɢᴇs ғʀᴏᴍ ɪɴғɪɴɪᴛʏ ᴛᴏ ᴛʜᴇ ɢɪᴠᴇɴ ᴄᴏɴғɪɢᴜʀᴀᴛɪᴏɴ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴏғ ᴛʜᴇ sʏsᴛᴇᴍ, ʜᴇɴᴄᴇ ᴛʜᴇ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴜ(Ɵ) ᴄᴀɴ ʙᴇ ᴀssᴏᴄɪᴀᴛᴇᴅ ᴛᴏ ᴛʜᴇ ɪɴᴄʟɪɴᴀᴛɪᴏɴ Ɵ ᴏғ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴜsɪɴɢ ᴛʜᴇ ᴀʙᴏᴠᴇ ʀᴇʟᴀᴛɪᴏɴ.
ғʀᴏᴍ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇϙᴜᴀᴛɪᴏɴ, ᴡᴇ ᴄᴀɴ sᴇᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴏғ ᴅɪᴘᴏʟᴇ ᴘʟᴀᴄᴇᴅ ɪɴ ᴀɴ ᴇxᴛᴇʀɴᴀʟ ғɪᴇʟᴅ ɪs ᴢᴇʀᴏ ᴡʜᴇɴ ᴛʜᴇ ᴀɴɢʟᴇ Ɵ ɪs ᴇϙᴜᴀʟ ᴛᴏ 90° ᴏʀ ᴡʜᴇɴ ᴛʜᴇ ᴅɪᴘᴏʟᴇ ᴍᴀᴋᴇs ᴀɴ ᴀɴɢʟᴇ ᴏғ 90°.
ᴄᴏɴsɪᴅᴇʀɪɴɢ ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴀɴɢʟᴇ ᴛᴏ ʙᴇ ᴛʜᴇ ᴀɴɢʟᴇ ᴀᴛ ᴡʜɪᴄʜ ᴛʜᴇ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ɪs ᴢᴇʀᴏ, ᴛʜᴇ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴏғ ᴛʜᴇ sʏsᴛᴇᴍ ᴄᴀɴ ʙᴇ ɢɪᴠᴇɴ ᴀs,
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