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Parents could be prosecuted if their children take explicit photographs or videos of themselves or anyone else aged under 18.
Police have issued the warning amid a growing trend of sexual images being shared with large groups of people on social media sites.
Officers have received a surge in reports, with 40 children being identified as having had nude selfies of them posted online in Thanet alone.
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They say so-called Bait Out pages are being set up to encourage young people to share images and get involved in sexual gossip and bullying.
Kent Police Supt Susie Harper said: “If a child’s mobile phone contract is in his or her parent’s name, then the parent can be liable for what the phone is used for, and any indecent material that is saved or sent from it.
“That could mean police turning up at the family home with a search warrant, property being seized, potential arrests and innocent people being suspected of serious offences.
“I’m not raising awareness to scaremonger, and our first priority is to safeguard young people and protect them from harm and there are many places we can signpost then to for independent help and advice.
“I also think it’s important for parents to be aware about the ways their children might be vulnerable to these things and what they can do about it.”
Police say children in Kent are at risk of having indecent images or information about them being widely circulated online.
This can be due to an increase in 'self-generated indecent images', images that may have been taken by young people as a result of sexting or sharing nude selfies between friends or as part of a relationship.
They say although sexting can be seen by young people as harmless, creating or sharing indecent images of a child below the age of 18 is illegal, even if the person doing it is themselves a child, and they could get a criminal record.
A young person will be breaking the law if they:
Police say whilst they do not wish to unnecessarily criminalise young people, this could potentially affect a child’s reputation, education and future employment prospects, for example, if they are named on a crime report or receive a caution or other criminal sanction.
"If a child's mobile phone contract is in his or her parent's name, then the parent can be liable for what the phone is used for" - Supt Susie Harper
They warned taking, sharing or receiving these images can also have a long-lasting impact on a child’s emotional health and wellbeing - causing emotional distress, an increased risk of them receiving negative comments and bullying, and putting them at risk of abuse and exploitation.
Police youth engagement officers will be liaising with schools to raise awareness of the consequences of taking, sharing and/or receiving of nude images of other young people as well as signposting to sources of support.
Officers would also like to encourage all parents and carers to speak to their children about the possible consequences of taking and sharing nude images of themselves or other young people.
Supt Susie Harper added: “I appreciate this is a very sensitive issue for parents and carers to raise, but there are a number of places where they can get expert advice on talking to their children about these issues, including the Kent Police website."