How to write error log or exception into file in java

Using log4j you can log exceptiosn quite easily:

try {
    ...
} catch(Exception e) {
    log.error("An exception! Oops!", e);
}

First read log4j Manual, it's easy to configure a rolling log file. You do not have to do any explicit file operations.

#SET LEVEL of ROOT-LOGGER, you will like to have Debug in local, but in prod you may just want WARN and ABOVE. This setting is done here!
log4j.rootLogger=debug, stdout, R

log4j.appender.stdout=org.apache.log4j.ConsoleAppender
log4j.appender.stdout.layout=org.apache.log4j.PatternLayout

# Pattern to output the caller's file name and line number. (basically, format of log)
log4j.appender.stdout.layout.ConversionPattern=%5p [%t] (%F:%L) - %m%n

# THIS IS WHERE YOU WILL HAVE ALL THE LOG WRITTEN
log4j.appender.R=org.apache.log4j.RollingFileAppender
log4j.appender.R.File=/var/log/applogs/example.log

# Maximum size of log file, usually we keep 10MB
log4j.appender.R.MaxFileSize=100KB
# Keep one backup file, usually we keep 10
log4j.appender.R.MaxBackupIndex=1

log4j.appender.R.layout=org.apache.log4j.PatternLayout
log4j.appender.R.layout.ConversionPattern=%p %t %c - %m%n

Second, whenever you catch an exception, do like this

public class MyClass{

  private static Logger logger = Logger.getLogger(MyClass.class);

  public ReturnType myMethod(Param p, Param2 p2) {
    ....
    ....
    try {
      ..    
    } catch(MyException e) {
       logger.log("Exceptions happen!", e); //this will put all the details in log file configured earlier
    }
    ....
  }

  ....
}

It worth reading the manual. Even better read Complete log4j Manual