Copy and paste the following script.
<script language="ecmascript" type="text/ecmascript">
var fieldCollection;
var field;
var list;
function fieldRequired() {
var clientContext = SP.ClientContext.get_current();
if (clientContext != undefined && clientContext != null) {
var webSite = clientContext.get_web();
this.list = webSite.get_lists().getByTitle("List Request");
this.fieldCollection = list.get_fields();
this.field = fieldCollection.getByTitle("Date");
this.field.set_required(true);
this.field.update();
clientContext.load(this.field);
clientContext.executeQueryAsync(Function.createDelegate(this, this.OnLoadSuccess), Function.createDelegate(this, this.OnLoadFailed));
}
}
function OnLoadSuccess(sender, args) {
alert(this.field.get_required());
}
function OnLoadFailed(sender, args) {
alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
}</script>
<input id="btnFieldRequired" onclick="fieldRequired()" type="button" value="Set Required Field" />