Final answer:
Yes, S∩T is a subring of R. The statement about the electric field requires more information.
Step-by-step explanation:
In the case of (a), if S and T are subrings of R, then S∩T is also a subring of R. To prove this, we can use the subring test, which states that for S∩T to be a subring of R, it must satisfy three conditions: (1) it is closed under addition, (2) it is closed under multiplication, and (3) it contains the additive identity of R. Since S and T are both subrings of R, they already satisfy these conditions, so S∩T will also satisfy them and therefore be a subring of R.
In the case of (d), the statement that there is a point between S and T where the electric field is zero depends on the specific situation being considered. Without more information, it is not possible to determine the truth of this statement.