Answer:
The charge-to-mass ratio of the particle is 5.7 × 10⁵ C/kg
Explanation:
From the formulae
F = qvB and F = mv²/r
Where F is Force
q is charge
v is speed
B is magnetic field strength
m is mass
and r is radius
Then,
qvB = mv²/r
qB = mv/r
We can write that
q/m = v/rB ---- (1)
Also
From Electric force formula
F = Eq
Where E is the electric field
and magnetic force formula
F = Bqv
Since, electric force = magnetic force
Then, Eq = Bqv
E = Bv
∴ v = E/B
Substitute v = E/B into equation (1)
q/m = (E/B)/rB
∴ q/m = E/rB²
(NOTE: q/m is the charge to mass ratio)
From the question,
E = 3.10 ×10³ N/C
r = 4.20 cm = 0.0420 m
B = 0.360 T
Hence,
q/m = 3.10 ×10³ / 0.0420 × (0.360)²
q/m = 569517.9306 C/kg
q/m = 5.7 × 10⁵ C/kg
Hence, the charge-to-mass ratio of the particle is 5.7 × 10⁵ C/kg.
