1. Condition for undeflected motion

If the charged particle continues moving along the $x$-axis without deviation, then the net Lorentz force must be zero:

So,

Hence, the electric and magnetic forces must be equal in magnitude and opposite in direction.

2. Given data

• Charge: $q = -16 \times 10^{-18}\,\text{C}$
• Speed: $v = 10\,\text{m s}^{-1}$
• Electric field magnitude: $E = 10^4\,\text{V/m}$ along negative $z$-axis
• Magnetic field $\vec B$ is along the $y$-axis

3. Direction of magnetic force

Velocity is along $+x$ and magnetic field is along $+y$.

So,

Thus $\vec v \times \vec B$ is along $+z$.

But the charge is negative, so magnetic force

will be along $-z$.

Electric field is along $-z$, so electric force on a negative charge is opposite to $\vec E$, i.e. along $+z$.

Therefore, electric and magnetic forces are opposite, so they can cancel. This is consistent.

4. Equating magnitudes

For no deflection,

Cancel $|q|$:

So,

Since $1\,\text{T} = 1\,\text{Wb/m}^2$,

5. Option check

• A: $10^3\,\text{Wb/m}^2$ ✅
• B: $10^5\,\text{Wb/m}^2$ ❌
• C: $10^{16}\,\text{Wb/m}^2$ ❌
• D: $10^{-3}\,\text{Wb/m}^2$ ❌

So the correct option is A.