US President Donald Trump’s re-election campaign is running hundreds of Facebook advertisements pushing an unfounded conspiracy theory that Joe Biden cheated during the first US presidential debate.

The adverts show the Democratic Party challenger with an earpiece, and say that he refused to have his ears checked for devices prior to the debate.

The Biden campaign rejected the claims.

The Trump campaign adverts ask: “Why won’t Sleepy Joe commit to an ear test?” and “Who is in Joe’s ear?”

Accusations that presidential candidates have received debate help via hidden hearing devices are familiar, albeit unproven. Such allegations have been levelled against both Republican and Democratic candidates in the past.

Prior to Tuesday’s debate, the rumour about Mr Biden’s supposed earpiece was circulating on several social networks, and was being promoted by the Trump campaign.

The advertising campaign was launched after the debate, and also promotes two other baseless but widely shared rumours about Mr Biden. One suggested he asked for breaks during the debate, and another accused him of refusing a “drug test”.

The photo featured in the advert is not from Tuesday’s debate. It was first shared online in September 2019.

In a number of the adverts, it has been doctored to show Mr Biden wearing wireless Apple headphones. This was not the case in the original image. Some versions circle the ear featuring the headphone.

By Wednesday evening, there were at least 15 different versions of the advert, and according to Facebook’s Ad Library, they had reached at least 10 million users.

Facebook has pledged to label posts containing voting misinformation and point users towards accurate information ahead of the election. However its policy does not involve fact-checking political speech, including in advertisements.

The company declined to comment about the latest Trump ad campaign.

Hours before the debate, the claims went viral on Facebook and YouTube.

Identical memes were pushed by a number of popular Facebook pages with names such as US Conservative and Unhinged Left. They claimed “Joe Biden should be inspected for a hidden earpiece as well as submit to a drug test before the debate”.

These memes are subject to fact-checks – and some have had warning labels applied to them on Facebook.

They were further amplified by supporters of QAnon, an unfounded a conspiracy theory that claims President Trump is fighting a secret war against elite Satan-worshipping paedophiles.

Those who believe in QAnon are known for promoting political disinformation on social media which targets opponents of the president. They shared close-up pictures of Mr Biden’s ears, alleging a listening device was visible.

During the debate, some also shared photos of a fold in Mr Biden’s shirt, claiming it was caused by a wire, and of a supposed device on his wrist, where he wears a rosary in memory of his late son Beau.

Democratic candidate Hillary Clinton faced similar unfounded claims ahead of the 2016 presidential election.

In 2004, rumours circulated among left-wing sites and blogs that President George W Bush was being aided by a secret earpiece.

None of those allegations were found to be true.

Even if a candidate did wear an earpiece, any advantage would be questionable. As TV and radio presenters can attest, listening to someone while simultaneously talking during the back-and-forth of a live event is a difficult skill to master.

The US Department of Commerce has written to American suppliers of China’s biggest chip manufacturer, warning them of “unprecedented risks” that their products could be used by the Chinese military.

The letter reminds the firms they must apply for licences to ship controlled items to Shanghai-based SMIC.

But it does not appear that Washington has decided whether or not to add the firm to a trade blacklist.

SMIC has denied any military links.

And it said it had not received any formal notice of new restrictions from the US.

But the latest action caused Semiconductor Manufacturing International Corporation’s shares to drop about 7% in Hong Kong trade.

The fall followed a steeper decline earlier this month when the Pentagon first revealed it had proposed tougher restrictions against the business, including adding it to the government’s Entity List.

That would prevent any company selling goods or services to SMIC that involved US intellectual property without first getting special permission.

Such a step has already been taken against SMIC’s biggest client – Huawei – which has caused major disruption to the telecoms kit-maker’s business.

But one industry analyst suggested the latest move indicated the US was increasingly focused on SMIC itself.

“Denial of US semiconductor manufacturing equipment would put SMIC at a severe disadvantage, because most of that technology comes from American sources,” explained Jim Tully.

“China could aim to become self-sufficient in these technologies over the longer term, but it seems to me that it would take 10-plus years to do so.

“And in the short term, the equipment and related software SMIC already uses still needs ongoing support and maintenance from its producers.”

This has led to speculation that SMIC’s survival may now be at stake.

SMIC was founded in 2000, and has since become the most prominent chip-making foundry in mainland China.

Until recently, it was viewed as being a beneficiary of rising US-China tension because it was expected to benefit from Beijing’s drive to make the country’s tech sector self-sufficient.

The firm has raised close to $10bn (£7.7bn) this year via a share sale and other means to expand its operations.

In addition to Huawei, SMIC’s clients include lesser-known Chinese chip designers including Gigadevice and Unisoc, as well as international companies including Qualcomm and Broadcom.

However, its most advanced products are said to lag two generations behind what rival manufacturers – including Taiwan Semiconductor Manufacturing Company (TSMC) and South Korea’s Samsung – are capable of, because SMIC cannot currently make transistors as small as they can. This means its products are not suitable to be the state-of-the-art processors in the latest smartphones or other advanced gadgets.

The reason for this is in part due to existing restrictions Washington has imposed on the firm.

At present, the only way to make the most advanced logic chips is to use equipment made by a Dutch company, ASML.

A spokesman for ASML declined to comment when asked by the BBC whether the deal was still in limbo.

Adding SMIC to the US Entity List would prevent the Chinese firm sourcing hardware, software and chemical materials from other suppliers.

For now, the company is hoping to avoid that outcome by clearly denying it supplies products to the People’s Liberation Army.

“Any assumption of the company’s ties with the Chinese military are untrue statements and false accusations,” it has said.

But this has been called into question by others.

The government says more than 10 million people across England and Wales have downloaded the NHS Covid-19 app since its launch on 24 September.

The Department for Health and Social Care has emphasised that using it is voluntary.

It also says the guidance the app issues about whether to self-isolate or get a test is not enforceable by law.

The app itself may look simple, but it has thrown up lots of questions about how it works and what its limits are.

Here’s our attempt to answer some of your queries:

A feature of the app is its ability to scan a QR barcode to log in at a pub, restaurant or other location – an alternative to actually handing over your contact details to that business on a paper log or website (though in Wales you still need to do both).

But people have noticed that while you can log in you cannot log out, and even if you soon leave the app thinks you are still there until midnight unless you log in somewhere else.

The point however of the QR scan is just to register your presence at that location rather than your proximity to someone infectious, which is registered via the Bluetooth contact-tracing feature.

If the location is later identified as a virus hotspot then an alert may be sent out to anyone who scanned a QR code there – not to self-isolate, but to be on the lookout for any symptoms of the virus.

But you cannot be alerted that somebody arrived in the pub hours after you left, and they later tested positive, because your phones could not have been physically close to each other at the same time.

But some are asking why there isn’t a code for a negative result, especially as a self-isolation countdown begins as soon as someone registers that they have symptoms.

There seem to be a couple of answers. If you’ve been told to self-isolate because you have been in contact with an infected person, then you are supposed to do so regardless of whether you test negative yourself.

If you are the potentially infected person, then nobody will be notified via the app without a positive result. However, it does mean you have to live with the timer as it cannot be de-activated – but as we said, adhering to this is not legally enforceable.

Then there’s the fact that the intention is that you now arrange your test via the app after reporting symptoms. In this case, the results – positive, negative or void, (which means a retest is needed) – will be registered automatically in the app without any need to enter a code.

When you first download the app it asks for part of your postcode. You then get a message on the homescreen telling you what the risk level in your area is.

Why doesn’t this change when you move somewhere – for instance when a student leaves home to go to university?

Right at the beginning of the app’s development, privacy campaigners expressed concern about the government tracking people – and a promise was made that location tracking would not be a feature of this app.

There is however a way of changing that postcode without reinstalling the app. Go to “About this app”, then “Manage my data” and you will then be able to edit your postcode.

A number of people – in particular those with iPhones earlier than the 6S which went on sale in 2015 – are finding that they are unable to install the app on their phone.

This is not due to a decision by the app’s developers but is a limitation imposed by Apple and Google. They have designed the toolkit on which this and many other contact-tracing apps around the world are based – and they have determined that older phones would not be suitable for running the technology behind the app.

A number of people have reported getting notifications about exposure to the virus and then not being able to find out what they need to do next.

Some are confused because of the way they are written – including the phrase “exposure date, duration and signal strength have been saved”.

“These are default messages from Apple and Google. There is no need to be concerned if you miss or overlook them, they are just visible to remind you that the functionality is on and working. You’re currently not able to turn off these default Apple and Google notifications.

“Important messages from the NHS Covid-19 app will always be visible to you from inside the app.”