a) A singly charged positive ion with a mass of 6.68*10^-27 kg moves clockwise in a circular path of radius 3 cm with a speed of 10000m/s. Find the direction and strength of magnetic field. b) Find the direction and strength of magnetic field if the ion moves counterclockwise.
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To find the direction and strength of the magnetic field in both cases, we can use the formula for the magnetic field due to a charged particle moving in a circular path:
B = (μ₀ * q * v) / r
Where:
- B is the magnetic field
- μ₀ is the permeability of free space (constant)
- q is the charge of the particle
- v is the velocity of the particle
- r is the radius of the circular path
a) For the singly charged positive ion moving clockwise:
q = +e (charge of a proton)
v = 10000 m/s (velocity)
r = 0.03 m (radius)
Plugging these values into the formula, we get:
B = (4π * 10^-7 T*m/A * 1.6 * 10^-19 C * 10000 m/s) / 0.03 m
Simplifying the calculation gives:
B ≈ 0.013 T (Tesla)
Since the ion is moving clockwise, the direction of the magnetic field would be perpendicular to the plane of motion and pointing downwards (towards the center of the circular path).
b) For the ion moving counterclockwise, the only change is the direction of the velocity. So, we can use the same values for q, r, and v as in the previous calculation.
Plugging these values into the formula, we get:
B = (4π * 10^-7 T*m/A * 1.6 * 10^-19 C * 10000 m/s) / 0.03 m
Simplifying the calculation again gives:
B ≈ 0.013 T (Tesla)
The magnitude of the magnetic field does not change since the magnitude of the velocity is the same. However, the direction of the magnetic field is now pointing upwards (away from the center of the circular path) because the direction of the velocity has reversed.
So, in summary:
a) For the ion moving clockwise, the magnetic field is approximately 0.013 T and points downwards.
b) For the ion moving counterclockwise, the magnetic field is approximately 0.013 T and points upwards.