Question

A thin conducting ring of radius R is given a charge + The electric field at the center O of the ring due to the charge on the part AKB of the ring is E. The electric field at the center due to the charge on the part ACDB of the ring is

• A. E along KO
• B. 3E along OK
• C. 3E along KO
• D. E along OK

Answer 1

The Correct Option is D

To solve this problem, we first need to analyze the scenario described: a charged conducting ring is divided into two parts by points A, K, B, C, D, with a charge distribution affecting the electric field at the center O.

The total charge on the ring creates a symmetrical electric field at the center O. This field can be decomposed based on the segments of the ring, namely the segments AKB and ACDB. Let us evaluate the contribution of each segment to the net electric field at the center:

1. The problem states that the electric field at the center O due to the charge on part AKB is E. This means that the electric field due to AKB is directed along a specific direction, let's assume along KO, as per the options given.
2. The remaining part of the ring, ACDB, thus contributes to the net electric field in the opposite direction with magnitude greater than E given the difference in length. Typically, if each part (half) of the ring is symmetrical, they produce equal magnitude but opposite direction electric fields. However, since here one part is three times the other, the field due to ACDB will be thrice that of AKB.
3. Thus, the electric field due to ACDB is 3E, but it acts along the line opposite to that of AKB. Since AKB's field is along KO, ACDB's field should be along OK (opposite direction).

Based on the above logic and symmetry, the electric field at the center due to the charge on part ACDB is E along OK.

Therefore, the correct option is: E along OK.