Question

A sodium ion (Na+) moves in the xy-plane with a speed of 2.70 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 2.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration.

What is the magnitude (in N) of the magnetic force acting on the ion?
(A) 0.01215 N
(B) 0.00765 N
(C) 0.00495 N
(D) 0.00225 N

Answer 1

0.00765 N is the magnitude (in N) of the magnetic force acting on the ion. Therefore, the correct option is B.

Step-by-step explanation:

The magnitude of the magnetic force (F) acting on a sodium ion moving in a magnetic field is given by F = qvB, where q is the charge of the ion, v is its velocity, and B is the magnetic field strength.

Given:

Charge of sodium ion (q) = 1.60 × 10⁻¹⁹ C,

Velocity (v) = 2.70 × 10³ m/s,

Magnetic field strength (B) = 2.25 × 10⁻⁵ T.

Substitute these values into the formula:

F = (1.60 × 10⁻¹⁹ C) × (2.70 × 10³ m/s) × (2.25 × 10⁻⁵ T).

Calculating this yields F = 0.00765 N.

Therefore, the correct answer is (B) 0.00765 N.