Question

An electron moves through a uniform magnetic field given by B=(Bₓi+3Bₓj)T. At a particular instant, the electron has velocity v=(3.0i+5.0j)m/s and the magnetic force acting on it is (6.4*10⁻¹⁹ N)k. Find Bx.

Answer 1

To find Bₓ for an electron moving in a uniform magnetic field with a specified velocity and force, the cross product of the velocity and magnetic field vectors is used, showing that Bₓ = 1.0 T.

Step-by-step explanation:

To find the value of Bₓ in a uniform magnetic field given as B = (Bₓi+3Bₓj)T, where an electron with a charge (e) of approximately -1.6 × 10⁻¹⁹ C is moving with velocity v = (3.0i + 5.0j) m/s and experiences a magnetic force of (6.4 × 10⁻¹⁹ N)k, we use the formula for the magnetic force on a moving charge in a magnetic field, which is F = e v x B. The cross product of v and B gives us the i, j, and k components of the force. However, in this case, only the k component of the force is provided, so we can use this to solve for Bₓ.

The cross product of the vectors is:

Since the force's k component is given as 6.4 × 10⁻¹⁹ N, we have:

4Bₓe = 6.4 × 10⁻¹⁹ N

Substitute the known value for e and solve for Bₓ:

4Bₓ(-1.6 × 10⁻¹⁹ C) = 6.4 × 10⁻¹⁹ N

Bₓ = -(6.4 × 10⁻¹⁹ N) / (4 × -1.6 × 10⁻¹⁹ C)

Bₓ = 1.0 T