Final answer:
The magnitude of the electric field at the midpoint between two charged rings is calculated based on the contribution from both charges, and the direction is towards the negatively charged ring. The magnitude of the force on a proton at this point is found by multiplying the electric field by the charge of the proton, and the force direction is the same as that of the electric field.
Step-by-step explanation:
Magnitude and Direction of Electric Field and Force on a Proton
The magnitude of the electric field (E) at the midpoint between two charged rings can be found by considering the contribution of the field from each ring and noting that the electric field due to a ring of charge at a point along its axis is given by an expression derived from Coulomb's law and the geometry of a ring.
Since the problem specifies the left ring has a charge of −30 nC and the right ring has a charge of +30 nC, the electric fields created by both rings at the midpoint will point in the same direction — towards the negatively charged ring.
The magnitude of the field can be calculated by using the superposition principle, which involves adding the electric field contributions from each ring separately.
To find the magnitude of the force (F) on a proton at the midpoint, we use Coulomb's law, where the force is the product of the electric field and the charge of the proton.
Given the charge of a proton is +e (approximately +1.6 x 10−12 C) and knowing the electric field, the force can be easily computed. The direction of this force will be the same as the direction of the electric field since a proton has a positive charge.