Positive singly charged ions travel to the right through uniform crossed fields. The electric field is 64800 V m⁻¹ upward and the magnetic field is 0.18 T out of the page. Neglect gravity. (a) Determine the undeflected speed. (b) Predict the initial deflection for ions travelling at 80% of that speed and for negative singly charged ions at the original speed. Use |q| = 1.602 × 10⁻¹⁹ C.

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Selected speed 3.600 × 10^5 m s⁻¹. Slower positive ions initially deflect upward; negative ions at the selected speed remain undeflected. For a positive charge travelling right, v × B points downward when B is out of the page. Its magnetic force therefore opposes the upward electric force, making cancellation possible. Set qE = qvB for zero net transverse force. Charge cancels, so v = E/B = 3.600 × 10^5 m s⁻¹; neither the ion mass nor charge magnitude determines the selected speed. At 0.8 of this speed the magnetic force is only 0.8qE. The net force is 0.2qE upward, with magnitude 2.076 × 10^-15 N for the stated charge. For negative ions both the electric and magnetic forces reverse. Their magnitudes remain equal at E/B, so the two reversed forces still cancel and the beam remains undeflected. The unit check is (V m⁻¹)/T = m s⁻¹. The selector chooses velocity through force balance; it does not require magnetic forces to do work on the moving charge.

Select a charged-particle speed · set 8

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