1.A proton enters a 2.0 X 10^-2 T magnetic field with a speed of 5.8 X 10^4 m/s. What is the radius of the circular path it follows?
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2.Electrons moving at 3.5 X 10^4 m/s pass through an electric field with an intensity of 5.6 X 10^3 N/C. How large a magnetic field must the electrons also experience for their path to be undeflected?
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You can derive this by setting centripetal force=magnetic force
mv^2/r=qBv
1. To determine the radius of the circular path a proton follows in a magnetic field, we can use the formula for the magnetic force on a charged particle moving through a magnetic field, set equal to the centripetal force.
The formula is:
magnetic force = centripetal force
qvB = mv²/r
Where:
q = charge of the particle (in this case, the charge of a proton is 1.6 × 10⁻¹⁹ C)
v = velocity of the proton (in this case, 5.8 × 10⁴ m/s)
B = magnetic field strength (in this case, 2.0 × 10⁻² T)
m = mass of the proton (1.67 × 10⁻²⁷ kg)
r = radius of the circular path (what we need to find)
To find the radius (r), we can rearrange the equation:
r = mv / (qB)
Now plug in the given values:
r = (1.67 × 10⁻²⁷ kg) × (5.8 × 10⁴ m/s) / (1.6 × 10⁻¹⁹ C) × (2.0 × 10⁻² T)
2. To determine the magnitude of the magnetic field the electrons must experience for their path to be undeflected by the electric field, we can set the magnetic force equal to the electric force.
The formula is:
magnetic force = electric force
qvB = Eq
Where:
q = charge of the electron (in this case, the charge of an electron is -1.6 × 10⁻¹⁹ C)
v = velocity of the electrons (in this case, 3.5 × 10⁴ m/s)
B = magnetic field strength (what we need to find)
E = electric field strength (in this case, 5.6 × 10³ N/C)
To find the magnetic field (B), we can rearrange the equation:
B = E / (qv)
Now plug in the given values:
B = (5.6 × 10³ N/C) / ((-1.6 × 10⁻¹⁹ C) × (3.5 × 10⁴ m/s))
After performing the necessary calculations, you will find the radius of the circular path in question 1 and the required magnetic field strength in question 2.