An experimenter's logbook contains the following entry: "a charged particle is projected in a magnetic field of (7.0 i - 3.0 j ) 10⁻³ T . The acceleration of the particle is determined to be ( i + 7.0 j ) 10⁻⁶ m s ⁻² ". The number to the left of i in the latter expression is illegible. What could this number be?

Step-by-step solution

The magnetic force on a moving charged particle is given by F = q( v B ) . Since the magnetic force is always perpendicular to the magnetic field, the acceleration a of the particle must also be perpendicular to B . Therefore, the dot product of acceleration and magnetic field must be zero, a B = 0 . Given B = (7.0 i - 3.0 j ) 10⁻³ T and a = (x i + 7.0 j ) 10⁻⁶ m s ⁻² . Taking the dot product: (x i + 7.0 j ) (7.0 i - 3.0 j ) = 0 7.0x - 21.0 = 0 x = 3.0 The missing number is 3.0 .