A uniform magnetic field of 0.20 × 10^ -3 T is present in space....

The magnetic scalar potential $V_m$ is related to the magnetic field $\vec{B}$ by the relation $\vec{B} = -\nabla V_m$.

The change in magnetic scalar potential $dV_m$ over a small displacement $d\vec{l}$ is given by $dV_m = -\vec{B} \cdot d\vec{l}$.

When moving along the direction of the magnetic field, the angle between $\vec{B}$ and $d\vec{l}$ is $0^{{}^{{}^{\circ}}}$, so $\vec{B} \cdot d\vec{l} = B dl$.

For a uniform magnetic field, the change in magnetic scalar potential over a distance $\Delta l$ is:

$\Delta V_m = -B \Delta l$

Given $B = 0.20 \times 10^{-3} \text{ T}$ and $\Delta l = 50 \text{ cm} = 0.50 \text{ m}$, we get:

$\Delta V_m = -(0.20 \times 10^{-3} \text{ T}) \times (0.50 \text{ m}) = -0.10 \times 10^{-3} \text{ T m}$

The negative sign indicates that the magnetic scalar potential decreases along the direction of the magnetic field. Therefore, it decreases by $0.10 \times 10^{-3} \text{ T m}$.