My father is an experimental physicist. I vividly remember him working numbers with a slide rule in the late 70s. When IBM PCs came out he got them for the lab, but the kind of thing he does does not require loads of data analysis–or not the kind of thing you’d need to code for. More important, I’d say, is plumbing and electrical ability, to build the apparatus.
My dad got a PHd in physics in the mid 1960s. I am pretty sure he was writing computer programs at during his studies to analyze the data from experiments. I definitely know he was writing programs as a working physicist when I was growing up in the mid 70s. He worked with particle accelerators.
I got my undergraduate degree in Physics in 1994. No coding required, unless you count using spreadsheets to convert data points to graphs.
I did take a semester of FORTRAN, but it was not required and not even part of the science department at all, the class was under the Business department along with COBOL.
The two semesters of grad school I went through had no programming/coding either,
I started my undergraduate physics degree in 1972.
I didn’t need to program for my freshman classes, but was certainly aware of the importance of programming and took my first programming course as a sophomore. At least I think it was a formal course. My memory of those days is weak. I worked on the remote terminal and wrote programs, that I am sure of. My first experience with the concept of JCL. 
By 1975 I was certainly using programs I wrote as examples in my classes. However, no programming was required-the classes were at a level where extensive calculations were not needed. But I and everyone in my department understood the importance of programming and that using programs for data collection and analysis was the wave of the future.
1970 physics undergrad, here. Before taking Physics 101, you had to pass a slide rule test and be co-enrolled in a BASIC class. Programming wasn’t officially part of physics, but you’d simply never be able to keep up if you couldn’t do at least a little programming of math functions.
Started Engineering and Science in 1977. The engineers had a compulsary FORTRAN subject. A physics major did not require any programming.
The problem would be, if you start out doing physics and maths, you still need some other small subject in first year to fill out your program. If you didn’t like Chemistry, and had no Biology, you might well wind up in Comp Sci 101, which was a very popular first year subject for that reason.
Microcomputers, not minicomputers. Minicomputers were the size of large filing cabinets or, at the very least, washing machines. Microcomputers, built around microprocessors, were the size of typwriters.
Carter studied nuclear engineering, not nuclear physics.
94 graduate , although I did physics with computational physics, so pretty much had to do ‘coding’ aka trying to get fortran to run a bunch of computational routines form a library of solvers.
My peers who were doing the applied physics course could have got by without any programming, although fortran, and spice were taught ( and obviously gnuplot)and when doing a degree in the UK, you do not get a whole lot of choice in what subjects you take.
Now Iwoudl imagine a physics student uses a whole lot of MatLab
This is my experience too - in fact it’s a bit of a running joke in my family that a Physics PhD is just another name for a Computing degree.
My own take on the OP … it’s not a totally insane idea, but I think the 40’s sounds a bit early for you to really say that coding was necessary for nuclear physics. Certainly a degree of engineering ability would have been helpful, maybe even necessary - mucking about with resistors and vacuum tubes and soldering irons, building your own lab equipment. That’s the sort of thing that morphed into low-level coding (low-level as in close to the hardware, not as in easy 
as the sort of equipment you used became more and more complex. By my dad’s era (nuclear physics PhD, early 60’s), yes, there was an awful lot of programming going on, and to take the question the other way round, if you were looking for someone who knew how to program, the Physics department would be high on your list of sources.
Definitely disagree with the concept that back in the day programming would have been left to professionals because it was difficult. There were no professionals back then - all the early pioneers of computing started out as something else - mathematicians, engineers, physicists. And yes, it was difficult compared to nowadays, but then, so was soldering your own lab equipment.
By the time I was studying Physics and Computing in the late 80’s there was a real Computing department, and I don’t know how old it was but it felt pretty recent - no more than a decade or so old, I’d say. And the links between computing and the hard sciences were pretty strong - we still had lecturers who were ex-physicists or ex-mathematicians, and I don’t think you would have been able to get through a Physics degree without doing at least some Fortran.
If I had to guess an answer to the OP’s question, I’d say “some time between the 50’s and the 70’s”, depending on your institution, your inclination, and your particular field of study.
I was in college in the early to mid 70s. Math majors were required to take the same introductory programming class as Computer Science majors. Physics majors had to take a different intro class oriented towards science, although both classes taught Fortran programming. There was yet a third intro class aimed at Business students. I think they learned COBOL programming.
This thread was just an excuse to flush out the doper physics grads wasn’t it? NAG routines was the name of the solvers I was trying to remember , complex algorithms written by smart people that solved mathematical problems , the art was to try and find the right one amongst a big pile of them, and then find the right one that didn’t sun the Sparc station into a toaster.
Even today, there are still many physicists who don’t do any programming. They’re mostly the older folks, but academics tend to retire only when forced to by health conditions such as death, so those older folks remain a significant part of the community.
I started my undergraduate physics degree in 89 and I remember watching computers take over the campus during my tenure there. I don’t think the seniors when I was a freshman had much in the way of coding education, but I was required to take more than a year and could program in basic, Fortran, and assembly language when I left in 94. Graduate school was even more intensive.
I attended Purdue 1967-71
Big on hard sciences, math, and (of course) engineering.
CS at that time was a bunch of weird guys with crew socks who hung out in the basement of the Math building (home of the CDC computer complex).
I started as an engineering student - there was no mention of CS anything - not even an overview course.
If engineers didn’t have to dirty their hands in (octal) assembly-level code or FORTRAN, I doubt that a Physics major would need to.
At this point, what need is there for a Physicist to code?
I understand that students learn things they will never actually use in their professional lives, but:
Whatever the problem, isn’t there, by now, an application on the shelf?
In 1970, the TVA drainage was being modeled on the CDC complex (I remember because TVA had “control point access” to the system, and would take it.
(control point - when a program returns control to the operating system. AKA “instantly” - the OS is what loads the program, and it only loads the page being executed. It needs to be invoked to load the next page. If your program was running, well, you should have thought of that, shouldn’t you?)
Hmmm… my dad’s pushing 90. I think he still has his HP67 (?) Calculator with the programmable sticks. he wrote a number of programs for them.
Typically, statistical functions like finding the best line fit from a massive amount of data points was the sort of initial programming done. Simulations - dividing a virtual item into discrete elements, then simulating the process - had to wait for bigger computers and more memory, unless you were the Manhattan project and had a room full of cardpunches, sorters, adders, and keypunch operators. Simulations became more common IIRC in the later 60’s.
Doh! My typo.
With the advent of microcomputers, you could write programs that would step through thousands to millions of increments of a process to follow how it got to a result.
Right, I should have clarified: Not all of the old-timers avoid computers, but most of the people who avoid computers are old-timers.
AFAIK, Carter did not study an academic/research course of nuclear physics, but went through the Navy’s (practical/applied) course for management and supervision of nuculur reactors. (Which is still an impressive facet of the man, but it doesn’t mean he was ready to work next to Feynman or Alvarez.)
I will note that our eldest got his degree in Physics from a major tech university, and has never worked in anything except programming, mostly large-scale web projects involving some degree of engineering need. I also worked with a lot of phys majors working as mechanical engineers, all of whom wrote their own extensions and modules for things like modeling programs.