Bad Power Supply?

Hi,

I have a MacBook Pro which is only a month or so old.

I have noticed that every time I plug the laptop into the power supply in a certain library in university the trackpad becomes much less responsive and starts jumping and lagging all over the screen, however as soon as I unplug the laptop this problem stops.

I am using the MacBook plug that came with the laptop.

I was wondering if this is simply the power supply or if there is something wrong with my battery.

Also should I avoid charging my laptop with this power supply?

Thanks.