Calculating Magnetic Force on a Moving Charge near an Infinite Straight Wire

[eestep]

Homework Statement

An infinite straight wire is located at origin of a coordinate system. It has a large current of 73 x 10⁷ amps running positive z direction. A point charge of -4 micro-Coulombs is moving at 3 x 10⁶ m/s in positive x direction at point x=1.9 m, y=4.5 m. What is magnitude of magnetic force on this charge in Newtons? Answer is 139.51.

Homework Equations

B=$$\mu0$$I/(2$$\pi$$r)
F_B=qvBsin$$\theta$$

The Attempt at a Solution

B=(4$$\pi$$ x 10^-7 Tm/A)(73 x 10⁷ A)/(2$$\pi$$)(4.88m)=29.89 T
F_B=(4 x 10^-6 C)(3 x 10⁶ m/s)(29.89 T)sin(67.11)

 

[SammyS]

θ is the angle from the direction of vector qv and to the direction of vector B.

sinθ is missing from your answer.

 

[gomunkul51]

Very simple: you didn't took into account that the velocity is not totally orthogonal to the direction of the magnetic field, i.e. you didn't multiplied with sinLaTeX Code: \\theta.

The direction of the magnetic field is tangential to the radius, your radius is the vector (1.9, 4.5)m, you need to find the orthogonal direction to this vector.

**@SammyS beat me to it :)