Two metal spheres A and B of radii a & b (a `lt` b) respectively are at a large distance apart. Each sphere carries a charge of 100`mu`O. the sphere are connected by a conducting wire, then

Options

A. Charge will flow from A to B
B. Charge will flow from B to A
C. NO charge flows in the wire
D. All charges will reside on the connecting wire

Answer

To solve the problem step by step, let's analyze the situation involving the two metal spheres A and B, which are connected by a conducting wire.

### Step 1: Understand the initial conditions
- We have two metal spheres, A and B, with radii \( a \) and \( b \) respectively, where \( a < b \).
- Each sphere carries a charge of \( Q = 100 \, \mu C \).

### Step 2: Calculate the electric potential of each sphere
The electric potential \( V \) on the surface of a charged sphere is given by the formula:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the radius of the sphere.

- For sphere A (radius \( a \)):
\[ V_A = \frac{k \cdot 100 \times 10^{-6}}{a} \]

- For sphere B (radius \( b \)):
\[ V_B = \frac{k \cdot 100 \times 10^{-6}}{b} \]

### Step 3: Compare the potentials
Since \( a < b \) and both spheres have the same charge \( Q \), we can compare the potentials:
- Since \( b > a \), it follows that:
\[ V_A > V_B \]
This means sphere A is at a higher potential than sphere B.

### Step 4: Determine the direction of charge flow
When two conductors are connected by a wire, charge flows from the higher potential to the lower potential. Therefore, charge will flow from sphere A to sphere B.

### Step 5: Conclusion
Thus, when the two spheres are connected by a conducting wire, the charge will flow from sphere A to sphere B.

### Final Answer
The charge will flow from sphere A to sphere B.

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