It seems common knowledge that a choke at the antenna feedpoint stops the outside of the coax shield from radiating when transmitting into the antenna. But what about stopping the outside of the coax shield from picking up noise and sending it to the receiver? Will that feedpoint choke do anything in that case? Or does one need another choke at the receiver end as well?
By the principle of reciprocity, if it works for transmit, it works for receive also.
Possibly if your receiver and transmitter are separate devices you may end up with a situation where no common-mode current was detectable on transmit, and yet common-mode signals did appear in the receiver. However with modern equipment having both receiver and transmitter in the same shielded enclosure, I don't expect this is likely to occur.
If you have any doubt, it should not be difficult to test. How to detect common-mode currents or “RF in the shack”? describes a way to make a common-mode current detector with a clamp-on ferrite bead. Replacing the diode detector with an oscillator turns it into a common-mode current injector. You could then clamp this injector somewhere on the feedline and measure the received power, then repeat with it clamped around something on the other side of the choke.
The difference of these measurements will give you a rough estimate of the common-mode isolation. While none of this is calibrated and the measurement setup is also subject to all kinds of leakage paths which will skew the results, you then at least have some number which can demonstrate some improvement if the tests are repeated again after adding an additional choke, running the feedline underground, or undertaking any other measures to suppress or isolate common mode currents.
An RF choke works exactly the same for transmit as it does for receive and will also block any noise or received signals induced in the outer of the coax from reaching the receiver.
Adding an RF choke at the receiver won't help with blocking any common mode current which exists on the outside of the coax as this current flows into the coax at the antenna end and adds to the current traveling towards the receiver on the inside of the shield of the coax.
A common mode choke at the antenna feedpoint will have little to no affect on whether received RF induces signals on the outside shield of a long (relative to the wavelength) coax.
If you disconnect and completely take down the antenna, but leave the coax up; then connect the coax shield to a receiver, it will still receive HF signals, likely less than a dozen dB down from when connected to the antenna. It’s wire in the air. Perpendicular far field RF will induce currents in it, even if exactly balanced near field EM doesn’t. Think long wire antenna.
A choke at the radio would be a better attenuator for this (blocking coax RFI/EMI pickup).
Other answers address well how to measure it and how it affects transmit, but there is little discussion of receive.
For transmit, the choke's purpose is to reduce external coupling between the antenna and the coax when the antenna needs to be balanced and the coax geometry might disturb this. The ideal location for the choke in this situation is at the antenna feedpoint where it is suppose to be balanced.
For receive, I assume you are asking if you can reduce received noise received by common mode -- presumably noise that the antenna itself wouldn't also receive. This would assume that some part of the coax shield is itself acting as an antenna. In this case, any part of the coax could do this. A choke at the receiver should reduce such noise, assuming the antenna isn't also getting that noise.
But note another answer in another question brought up the point that multiple chokes on the coax could accidentally create a resonant section which could amplify the noise instead. For example, the Carolina Windom adds 10m to the system by intentionally setting up a vertical 10m resonant section of coax between two chokes. As with many things in amateur radio, the best way to get a practical answer is to try it and maybe move it around a bit until you get best results.
Yes - and No !! The use of ferrite chokes for receive is far more critical than for transmit. Typically you have electric and magnetic fields in your schack originating in switch power supplies. Computers, lamps, almost anything these days.. The fields will induce currents on the outside of your coax and they will travel up to the feedpoint and enter your center conductor and then get into your RX. A feedpoint choke would present a series resistance and in that way reduce the interference to some extent - just like it attenuates the transmit current. On the TX side 10 dB of attenuation is plenty, but on the RX side you might want 30 dB or more. The trick is to place a second choke 0.25 wavelengths from the feedpoint along the feedline. For the current on the outside of the coax this is a high impedance point (because of the choke at the feedpoint) so this second choke has a multiplicative effect. Note that a choke half a wavelength from the feedpoint does not help much because it would sit on a high impedance point for currents along the feeder. I have uploaded 4 videos about related problems. Search the Internet for "Sensors sm5bsz" These videos might convey some useful ideas on how to manage currents on the coax screen for the receive side.