The rule is that the studs in any exterior or load-bearing wall may be notched, but no deeper than 25% of the width of the stud, or a hole no bigger than 40% of the width of the stud may be bored in it (you could pass the conduit or cable through the stud). There's an exception that you can notch 60% of the depth if the stud is doubled and no more than two successive studs are notched that deeply. Non-load-bearing studs can be notched up to 40% of the depth of the stud.
Also, you cannot notch the side of the studs that structural sheathing/plywood is affixed to (see shear walls).
Here's the seemingly relevant International Building Code section:
R602.6 Drilling and notching - studs. Any stud in an exterior wall or
bearing partition may be cut or notched to a depth not exceeding 25
percent of its width. Studs in nonbearing partitions may be notched to
a depth not to exceed 40 percent of a single stud width. Any stud may
be bored or drilled, provided that the diameter of the resulting hole
is no greater than 40 percent of the stud width, the edge of the hole
is no closer than 5/8 inch (15.9 mm) to the edge of the stud, and the
hole is not located in the same section as a cut or notch. See Figures
R602.6(1) and R602.6(2).
- A stud may be bored to a diameter not exceeding 60 percent of its width, provided that such studs located in exterior walls or bearing
partitions are doubled and that not more than two successive studs are
- Approved stud shoes may be used when installed in accordance with the manufacturers recommendation. R602.6.1 Drilling and notching of
top plate. When piping or ductwork is placed in or partly in an
exterior wall or interior load-bearingwall, necessitating cutting,
drilling or notching of the top plate by more than 50 percent of its
width, a galvanized metal tie of not less than 0.054 inches thick
(1.37mm) (16ga) and 11/2 inches (38mm) wide shall be fastened to each
plate across and to each side of the opening with not less than eight
16d nails at each side or equivalent. See Figure R602.6.1.
Exception: When the entire side of the wall with the notch or cut is covered by wood structural panel sheathing
Is this EMT (metal conduit)? I would consider putting protective metal nail plates over the notches, as well. If it isn't metal conduit, I'm pretty sure you have to use those plates.