An electron moves through a uniform electric field E = (2.60i + 5.90j) V/m and a uniform magnetic field B= 0.400k in m/s^2.) T.

Required:
a. Determine the acceleration of the electron when it has a velocity v= 8.0i m/s.
b. What If? For the electron moving along the x-axis in the fields in part (a), what speed (in m/s) would result in the electron also experiencing an acceleration directed along the x-axis?

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batolisis batolisis · Answer 1 · 2022-04-11T13:13:03+02:00

A) The acceleration of the electron along the x -axis is ; 4.57 * 10⁻¹¹ m /s²

B) The speed that would result in the electron experiencing an acceleration along the x-axis is 4.57 * 10⁻¹¹ * time m/s

Given Data :

Electric field ( E ) = ( 2.60i + 5.90j ) V/m

Magnetic field ( B ) = 0.400 k T

Velocity ( v ) = 8.0i m/s

Applying Lorentz force

F = q ( E + ( v * B ) )

= 1.6 * 10⁻¹⁹ ( 2.60 i + 5.90 j + ( 8.0 i * 0.4 k ) ) N

= 1.6 * 10⁻¹⁹ ( 2.60 i + 5.90 j + ( 3.2 ( -j ) ) N

= 1.6 * 10⁻¹⁹ ( 2.60 i + 2.70 j ) N

Ax = 4.57 * 10⁻¹¹ m /s²

Ax = Fx / Mc

= ( 1.6 * 10⁻¹⁹ * 2.60 ) / 9.1 * 10⁻³¹

= ( 4.16 * 10⁻¹⁹ ) / 9.1 * 10⁻³¹

= 0.457 * 10¹²

= 4.57 * 10⁻¹¹ m /s²

Therefore The speed that would result in the electron experiencing an acceleration along the x-axis is 4.57 * 10⁻¹¹ * time

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