There are a total of 13 Tesla cannons, or 14 if one counts the Beta Tesla cannon, but only a maximum of 11 (12 with Beta Tesla cannon) can be obtained in one play-through.
The first Tesla cannon can be acquired upon the Lone Wanderer's initial arrival at Adams Air Force Base. There will be a resupply crate directly to the player character's left near the wall upon exiting the Presidential metro.
Once one leaves Adams Air Force Base, if they did not blow up the Citadel and return there, 2 Tesla cannons can be found in the Citadel laboratory after finishing the quest Who Dares Wins, on a table in front of Liberty Prime's docking bay.
If one blew up the Citadel, they can find 2 Tesla cannons in the Citadel armory. If one did not blow up the Citadel they can pick the lock to get into the armory but there are no Tesla cannons there.
If one returns to Adams Air Force Base after Who Dares Wins, they can acquire 8 more Tesla cannons (4 in perfect condition, 4 in poor condition):
The first pair are before the Lone Wanderer reaches the hangars. Traveling northeast from the Adams Air Force Base Entrance towards the hangars, the 4th open-topped military truck in their path has a resupply crate in the back with a good and poor condition cannon and electron charge packs.
The second pair of cannons (along with some electron charge packs) is in a resupply crate between the first and second hangar on the way toward the mobile base crawler by the base of an Enclave barricade. To be clear, these two hangars are to the player character's right once they reach the airfield portion of the base, near 2 parked Vertibirds.
The third pair are in a resupply crate by the ramp leading to the covered catwalk between the second and third hangar on the way to the crawler.
The fourth pair are at the base of an Enclave barricade, between the crawler and the air control tower. The crate is inside the ring of Sandbags underneath a Brotherhood of Steel Paladin.
It is also possible to obtain an unlimited amount of Tesla cannons from Adams Air Force Base. This can only be done before one destroys the Mobile Base Crawler. Simply observe the battle between the Brotherhood of Steel and the Enclave and at some point a paladin will bring out a Tesla cannon. Go around the force field and loot his body when he dies, then go back and wait for another. Note that the other Brotherhood of Steel soldiers may loot him before the player character get there leaving only armor or ammunition.
The Tesla cannon has a "shocking effect" much like Jingwei's shocksword. After hitting an enemy with a blast from the cannon, they'll be surrounded by an electrical effect for a few seconds which will cause damage.
The Tesla cannon has a splash effect when the projectile strikes any hard surface, damaging all near impact. It is entirely possible and quite common for this weapon to strike multiple enemies. Be aware, though, that this effect will also harm the player character or any companion.
If one looks into the barrel, they can clearly see the Tesla coil, which is its main component.
Star Paladin Cross and Clover will equip the Tesla cannon when given with ammunition, however, please note that when the cannon is placed in their inventory along with ammunition, it will degrade as normal. By stunning her with Paralyzing Palm, Sydney will equip the Tesla cannon when given with ammunition and it will not degrade.
When in V.A.T.S., if one uses two shots, and the first shot doesn't kill an enemy, but the shocking effect does, one will still fire it again even though the enemy is already dead.
Killing an enemy with the shock effect does not count as a kill for the purposes of the Grim Reaper's Sprint perk. The player character's AP will not be refilled unless the enemy dies from the initial blast.
Interestingly enough, this weapon's laser, or rather its shock effect, passes through walls and other solid barriers (i.e. one can shoot the Citadel Laboratory wall next to the map and Rothchild may be knocked unconscious).
The Tesla cannon has a scripted effect attached to it that allows it to destroy airborne Vertibirds with a single shot, regardless of actual damage done.
The Tesla cannon tends to kill a stronger enemy (Enclave Hellfire trooper for instance) in 1-2 shots (1 with shock). Also note that the shock effect can harm the player and followers in close ranges. Try to aim for the enemy in the middle as the shock will soften up the enemies around it, then a more practical firearm can be used if desired.
xbox360pc If the player character kills an enemy with the splash damage effect alone, they may not earn XP for the kill, but this can use this to ones advantage. If a good character is killed by the shock damage after effects it will result in no karma loss or hostility from nearby non-player characters. One will also not receive any fingers or ears for enemies killed by the cannon's splash damage. 表达式错误：未预料的<操作符
xbox360 Occasionally while in third person the Tesla cannon will float off of the Lone Wanderer's back and stay suspended in mid air. This makes it impossible to use in third person and V.A.T.S., however the Tesla cannon will still work in first person. (This will fix itself after a while. However, there is nothing that one can do to fix it manually.) 表达式错误：未预料的<操作符
pc The Tesla cannon will not destroy a Vertibird in a single shot, unlike the console versions of the game. 表达式错误：未预料的<操作符