Magento Get Products by Category ID

categoryProductCollection.php

<?php

$_categoryId = 123;
$_limit = 10;

$_categoryModel = Mage::getModel('catalog/category');

$_category = $_categoryModel->load($_categoryId);

$_productCollection = $_category->getProductCollection()
    ->addAttributeToSelect('*')
    ->setPage(1, $_limit);

if ($_products->getSize()) {
    foreach ($_products as $_product) {
        var_dump($_product->getData());
    }
}