Her husband beats her and does not spend on her, and there is no Muslim judge in her city

Firstly:

If the husband does not spend on his wife, or he beats her, it is permissible for her to ask for divorce (talaaq). If he refuses to spend on her, the qaadi (Muslim judge) should force him to divorce her, and if he does not do that, then the judge may issue the divorce (talaaq) himself, so as to ward off harm from the wife.

It says in al-Mawsoo‘ah al-Fiqhiyyah (41/66):

The scholars differed, in the event that the husband is faced with financial difficulties and his wife does not want to stay with him, as to whether she has the right to ask for separation from him. There are two scholarly views:

The first view is that she does not have the right to ask for separation, and the husband does not have the right to prevent her from earning a living so that she can spend on herself. This is the view of Ibn Shubrumah, Hammaad ibn Abi Sulaymaan, ‘Ata’, az-Zuhri, al-Hasan, Ibn Abi Layla, and others. This is the view of the Hanafis.

The second view is that the woman has the right to ask for separation from her husband, because of his inability to spend on her, and if he refuses then the judge may separate them.

This is the view of the Maalikis; it is regarded as more likely to be correct by the Shaafa‘is, and is regarded as the correct view by the Hanbalis.

This separation is regarded as an annulment of the marriage by the Shaafa‘is and Hanbalis, and as a revocable divorce (talaaq) by the Maalikis. This was narrated from ‘Umar, Abu Hurayrah and Ibn ‘Umar (may Allah be pleased with them), and was the view of Sa‘eed ibn al-Musayyab, al-Hasan, Ishaaq, Abu Thawr, and others. End quote.

If this is the case when the husband is not well off, then it is more appropriate if the husband is well off but refuses to spend on his wife.

If there is a Muslim judge, then he may order the husband to spend on his wife and treat her kindly, then if he refuses to spend on her or he is not well off, and the wife wants a separation, the judge may order a separation.

Secondly:

If there is no Muslim judge, then a Muslim community leader takes his place, such as the imam of the main mosque, or the director of the Islamic centre. So you should take your case to them, and they can summon your husband and listen to what he has to say, then if he continues to behave in this manner, they may separate you.

If the imam of the mosque refuses to listen to you, then look for another Muslim leader in your country.

You do not have the right to annul the marriage contract by yourself, under any circumstances.

Al-‘Adawi said in his commentary on Kifaayah at-Taalib ar-Rabbaani (2/133):

Muslim community leaders may act in the stead of the judge in that case and in all other cases where it is not possible to find a judge, or if the judge is not of good character.

But in the case of a husband who is not proven to be poor, and he admits that he is well off, but he refuses to spend on his wife or to divorce her, then he should be made to issue a divorce, according to one opinion, and according to another opinion, he should be imprisoned until he agrees to spend on her.

If he is imprisoned and does not do that, then he should be made to issue a divorce. End quote.

With regard to the wording of the divorce, it is sufficient to say words that are indicative of that, such as saying, “We rule that So-and-so be divorced from her husband, So-and-so, because of his refusal to spend on her,” and the like.

And Allah knows best.