An electron beam enters a crossed-field velocity selector with magnetic and electric fields of 2.0 mt and 6.0×10^3 n/c, respectively. (a) what must the velocity of the electron beam be to traverse the crossed fields undeflected? if the electric field is turned off? (b) what is the acceleration of the electron beam? (c) what is the radius of the circular motion that results?

a)   v = 3 10⁶ m / s , b)   a = 1.055 10¹² m / s² , c)    r = 8.53 m

Explanation:

a) Let's use Newton's Second Law of Balance, so that electrons do not deviate

      - = 0

      =  

     q E = q v B

     v = E / B

Let's calculate

    v = 6.0 10³ / 2.0 10⁻³

    v = 3 10⁶ m / s

b) If the electric field is disconnected, the only force left is the magnetic one

    = m a

    q v B = m a

    a = q / m v B

    a = q / m (E / B) B

    a = q / m E

    a = 1.6 10⁻¹⁹ /9.1 10⁻³¹ 6.0 10³

    a = 1.055 10¹² m / s²

c) Acceleration is centripetal

    a = v² / r

    r = v² / a

    r = (3 10⁶)² /1.055 10¹²

    r = 8.53 m

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.