An 1800 watt induction hotplate will bring 4 gallons of wort/water to a rolling boil at a rate of ~2.5F per minute as long as there is a single layer of Reflectix insulation (the silver bubble wrap stuff) on the sides and lid of your kettle. Two layers of insulation is slightly faster. Heat radiating from handles, thermometers, ball valve, etc. are minimal. The biggest heat loss is around the rim of the kettle, so I keep mine covered with a couple towels while heating.
With an eight gallon kettle, if you keep the lid on the boil it is nearly as vigorous as propane. If the lid is completely off (which I do for the last half of the boil) then it rolls in the center, but not the entire surface area. With four gallons you can't get a boil over, with six gallons you better have your spray bottle ready.
The thermal efficiency of the 1800 watt max burton hotplate greatly outstrips any apartment-sized coil stove I have ever used. And if you have two 20amp circuits for your kitchen (you should, but *always* verify) then you can easily run the induction cooker plus say a 1000 watt immersion heater from amazon for $35. That will boil (slowly) 11 gallons of wort. Or you could build a 1600 watt heat stick and boild 11 gallons pretty quick.
If you need any more metrics, let me know. I had to move to a 300 square foot apartment for work for the next two years, so I have been really on the 'high efficiency, low space' angle.
tl;dr 5 gallon batch + induction burner == rawk