Question

An electron (mass 9 × 10⁻³¹ kg and charge 1.6 × 10⁻¹⁹ C) moving with speed c/100 (c = speed of light)is injected into a magnetic field `vecB` of magnitude 9 × 10⁻⁴ T perpendicular to its direction of motion. We wish to apply an uniform electric field `vecE` together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 10⁸ m s⁻¹).

विकल्प

• `vecE` is perpendicular to `vecB` and its magnitude is 27 × 10⁴ V m⁻¹.

• `vecE` is perpendicular to `vecB` and its magnitude is 27 × 10² V m⁻¹.

• `vecE` is parallel to `vecB` and its magnitude is 27 × 10² V m⁻¹.

• `vecE` is parallel to `vecB` and its magnitude is 27 × 10⁴ V m⁻¹.

Answer 1

`vecE` is perpendicular to `vecB` and its magnitude is 27 × 10² V m⁻¹.

Explanation:

If an electron does not deflect from its path, the net force on it should be zero.

F_e = F_m

eE = evB

v = `E/B`

`E = c/100 xx 9 xx 10^-4`

= `(3 xx 10^8)/100 xx 9 xx 10^-4`

= `(27 xx 10^4)/100`

= 27 × 10² V/m

`vecF  ⊥  vecB and vecF_m+ vecF_e = vec0`

`vecF_e = -vecF_m`

Hence, `vecE  ⊥  vecB`