Given

• Electron velocity is along positive $x$-axis: $\vec v = +\hat i$
• Magnetic field is along negative $z$-axis: $\vec B = -\hat k$

Magnetic force formula $\vec F = q(\vec v \times \vec B)$ For an electron, charge is negative: $q=-e$

Find $\vec v \times \vec B$ $\vec v \times \vec B = \hat i \times (-\hat k) = -(\hat i \times \hat k)$

Using cross-product relations: $\hat i \times \hat k = -\hat j$

Therefore, $\vec v \times \vec B = -(-\hat j)=\hat j$

So for a positive charge, force would be along positive $y$-axis.

Since the particle is an electron The electron has negative charge, so the force direction is opposite to $\hat j$: $\vec F = -e(\hat j)$ Hence force is along negative $y$-axis.

Therefore, statement B is correct and A is false.

Nature of motion The velocity is perpendicular to the magnetic field: $\vec v \perp \vec B$ In a uniform magnetic field, when $\vec v \perp \vec B$, the charged particle moves in a circular path.

Therefore, statement E is correct.

Check remaining statements

• C: "The electron will not experience any force" → false
• D: "The electron will continue to move along positive $x$-axis" → false, because magnetic force changes its direction continuously.

Correct combination Correct statements are B and E only.

From the given options, this corresponds to: $\boxed{\text{Option C}}$