Statement - 1 : For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is zero.Statement - 2 : For a non-uniformly charged thin circular ring with net charge zero, the electric field at any point on axis of the ring is zero.a)Statement - 1 is true, Statement - 2 is true and statement - 2 is correct explanation for statement - 1.b)Statement - 1 is true, Statement - 2 is true and statement - 2 is NOT correct explanation for statement - 1.c)Statement - 1 is true, statement - 2 is false.d)Statement - 1 is false, statement - 2 is true.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Note that electric potential is a scalar quantity whereas electric field is a vector quantity. If it is aid that the net charge on the ring is zero it means that the total positive charge is equal to the total negative charge. So, the potential due to positive charges and the potential due to negative charges gets cancelled each other, thus the net electric potential is zero. But in case of electric field it may not be zero because the electric field due to each charge is in a different direction from the rest due to which they will not cancel out.

Answer

**Explanation:**

**Statement 1: For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on the axis of the ring is zero.**

The electric potential at a point due to a ring of charge can be calculated using the formula:

V = k * Q / r

Where V is the electric potential, k is the electrostatic constant, Q is the charge on the ring, and r is the distance from the ring to the point.

In this case, the ring has a net charge of zero, which means Q = 0. Therefore, the formula becomes:

V = k * 0 / r = 0

Since the charge on the ring is zero, the electric potential at each point on the axis of the ring is indeed zero.

**Statement 2: For a non-uniformly charged thin circular ring with net charge zero, the electric field at any point on the axis of the ring is zero.**

The electric field at a point due to a ring of charge can be calculated using the formula:

E = k * Q * z / (2 * pi * r^3)

Where E is the electric field, k is the electrostatic constant, Q is the charge on the ring, z is the distance from the ring to the point along the axis, and r is the radius of the ring.

In this case, the ring has a net charge of zero, which means Q = 0. Therefore, the formula becomes:

E = k * 0 * z / (2 * pi * r^3) = 0

Since the charge on the ring is zero, the electric field at any point on the axis of the ring is indeed zero.

**Explanation of the Correct Answer:**

The correct answer is option C: Statement 1 is true, and statement 2 is false.

While statement 1 is true, as explained above, statement 2 is false. The electric field at any point on the axis of the ring is not zero, even if the net charge on the ring is zero. The electric field depends on the distribution of charge along the ring, and even a non-uniform distribution can result in a non-zero electric field at points on the axis of the ring.

Therefore, statement 2 is not a correct explanation for statement 1.

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