Given

• A uniform electric field $\vec E$ and a uniform magnetic field $\vec B$ act along the same direction.
• An electron is projected along the direction of these fields.

Magnetic force on the electron

The magnetic force is $\vec F_B = q(\vec v \times \vec B).$

Since the electron is moving along the same direction as $\vec B$, the angle between $\vec v$ and $\vec B$ is $0^\circ$.

Therefore, $\vec v \times \vec B = 0,$ so $\vec F_B = 0.$

Hence, the magnetic field does not deflect the electron either to the left or to the right.

So, options C and D are incorrect.

Electric force on the electron

The electric force is $\vec F_E = q\vec E.$

For an electron, $q = -e,$ therefore $\vec F_E = -e\vec E.$

This means the force on the electron is opposite to the direction of the electric field.

Effect on velocity

The electron is projected along the direction of the fields, i.e. along $\vec E$.

But the electric force on it is opposite to its motion. Therefore, the electron experiences a retardation, so its speed decreases.

Hence, its velocity will decrease.

Checking options

• A: its velocity will increase — Incorrect
• B: its velocity will decrease — Correct
• C: it will turn towards left — Incorrect
• D: it will turn towards right — Incorrect

Final answer

The correct option is B.