The charge of 'assault by beating' is used (instead of that of 'common assault') when there has been a battery, which is defined in law thus:
"A battery is committed when a person intentionally and recklessly applies unlawful force to another".
Note that momentarily gripping someone's arm would provide sufficient grounds for the action to be considered a 'battery'.
'Section 39' offences are 'summary only', which means that they must be dealt with in a magistrates court, not in a Crown Court. While there's theoretically the possibility of a prison sentence (of up to 6 months) the reality is that minor matters (such as the one you've allegedly been involved in) normally result in a fine (plus costs, plus a payment to the fund set up to support victims of crime), with the possibility of a period of unpaid work.
Chris