A magnetic dipole of dipole moment `10(hati+hatj+hatk)` is placed in a magnetic field `0.6hati+0.4hatj+0.5hatk` force acting on the dipole is -

Options

A. `hati+hatj-2hatk`
B. `hati+hatj+2hatk`
C. zero
D. None of these

Answer

To find the force acting on a magnetic dipole placed in a magnetic field, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Magnetic dipole moment, **m** = \(10(\hat{i} + \hat{j} + \hat{k})\)
- Magnetic field, **B** = \(0.6\hat{i} + 0.4\hat{j} + 0.5\hat{k}\)

2. **Understand the Nature of the Magnetic Field**:
- The magnetic field is uniform, meaning it does not change in strength or direction at different points in space.

3. **Determine the Force on the Magnetic Dipole**:
- The force **F** acting on a magnetic dipole in a uniform magnetic field is given by the formula:
\[ \mathbf{F} = \nabla (\mathbf{m} \cdot \mathbf{B}) \]
- However, in a uniform magnetic field, the force on the dipole is zero. This is because the gradient of the magnetic field is zero (there is no change in the magnetic field strength or direction).

4. **Calculate the Result**:
- Since the magnetic field is uniform, the net force acting on the dipole is:
\[ \mathbf{F} = 0 \]

### Final Answer:
The force acting on the dipole is **0**.

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