A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself

Options

A. Uniformly in the metal object
B. Uniformly on the surface of the object
C. Such that the potential energy of the system is minimised
D. Such that the total heat loss is minimised

Answer

To solve the problem of how a charge \( Q \) coulomb distributes itself on a solid piece of metal of irregular shape, we can follow these steps:

### Step 1: Understand the properties of conductors
In electrostatics, it is known that in electrostatic equilibrium, the electric field inside a conductor is zero. This is a fundamental property of conductors.

**Hint:** Remember that charges in a conductor will move until the electric field inside the conductor is zero.

### Step 2: Determine charge distribution
Since the electric field inside the conductor must be zero, any excess charge placed on a conductor will redistribute itself. For a solid conductor, this means that all the charge must reside on the surface of the conductor.

**Hint:** Think about how charges behave in a conductor and how they will move to achieve equilibrium.

### Step 3: Consider the shape of the conductor
The conductor in this case is of irregular shape. While the charge will still reside on the surface, the distribution of the charge will not be uniform due to the irregularities in the shape. The charge will distribute itself in such a way that the electric field is zero inside the conductor.

**Hint:** Irregular shapes lead to non-uniform charge distribution on the surface.

### Step 4: Minimize potential energy
Any process in nature tends to minimize potential energy. The charge distribution will occur in a manner that minimizes the potential energy of the system. This means that the distribution will not only be on the surface but will also be influenced by the shape of the conductor to achieve the lowest potential energy configuration.

**Hint:** Consider how systems tend to favor configurations that lower their potential energy.

### Step 5: Evaluate the options
Based on the understanding that the charge will distribute itself on the surface of the conductor in a non-uniform manner and that this distribution minimizes potential energy, we can evaluate the options given in the question.

1. Non-uniform distribution on the surface - This is correct.
2. Uniformly in the metal object - This is incorrect, as charges do not reside within the volume of a conductor.
3. Uniformly on the surface of the object - This is incorrect for irregular shapes.
4. Such that the potential energy is minimized - This is correct.
5. Such that the total heat loss is minimized - This is incorrect, as heat loss is not a factor in this scenario.

From the evaluation, the correct answer is that the charge distributes itself on the surface in a non-uniform manner such that the potential energy is minimized.

**Final Answer:** The charge will distribute itself on the surface of the conductor in a non-uniform manner such that the potential energy is minimized.