Question

An electron has a velocity of 1.50 km/s (in the positive x direction) and an acceleration of 2.00 ✕ 1012 m/s2 (in the positive z direction) in uniform electric and magnetic fields. If the electric field has a magnitude of strength of 18.0 N/C (in the positive z direction), determine the following components of the magnetic field. If a component cannot be determined, enter 'undetermined'.

Answer 1

see explanation

Step-by-step explanation:

Given that,

velocity of 1.50 km/s = 1.50 × 10³m/s

acceleration of 2.00 ✕ 1012 m/s2

electric field has a magnitude of strength of 18.0 N/C

`\bar F= q[\bar E + \bar V * \bar B]\\\\\bar F = [\bar E + \bar V * ( B_x \hat i +B_y \hat j +B_z \hat z )]\\\\\\m \bar a = [\bar E + \bar V * ( B_x \hat i +B_y \hat j +B_z \hat z )]`

`9.1 * 10^-^3^1 * 2* 10^1^2 \hat k=-1.6*10^-^1^9 \hat k [18\hat k+ 1.5* 10^3 \hat i * (B_x \hat i +B_y \hat j +B_z \hat k)]`
`42.2 * 10^-^1^9 \hat k = -2.4 * 10^1^6B_y \hat k + 2.4 * 10 ^1^6 \hat j B_z\\`

`B_x = undetermined`

`B_y = (42.2 * 10^-^1^9)/(-2.4 * 10^-^1^6) \\\\= - 0.0176 T`

`B_z = 0T`