A uniform magnetic field points north; its magnitude is 3.5 T. A proton with kinetic energy 6.0 × 10-13 J is moving vertically downward in this field. What is the magnetic force acting on it?
This is what I've done. The answer is incorrect. Please help me find out why.
3.5T to the north
KE=1/2MV^2
2(6.0X10^-13J)/1.673X10^-27 = V^2
V^2 = 7.17x10^14
sqrt (7.17e14) = 2.6e7
Thennn
(1.60e-19C)(2.6e7)(3.5T)(sin90degrees)
= 1.45e-11 to the east.
To the east is correct, but my numerical answer is not. Help?
To find the magnetic force acting on a particle with a given kinetic energy moving in a magnetic field, you need to consider the equation for the magnetic force. The formula for the magnetic force on a charged particle moving in a magnetic field is given by:
F = q * v * B * sin(θ)
Where:
- F is the magnetic force
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field strength
- θ is the angle between the velocity vector and the magnetic field vector
Let's go through the steps to find the correct answer:
1. Given information:
Magnetic field strength (B) = 3.5 T (pointing north)
Kinetic energy (KE) = 6.0 × 10^(-13) J
2. Calculate the velocity (v) of the proton:
Using the equation for kinetic energy, KE = (1/2)mv^2, where m is the mass of the proton (1.673 × 10^(-27) kg), we can rearrange the equation to solve for v.
KE = (1/2)mv^2
v^2 = 2KE / m
v^2 = (2 * 6.0 × 10^(-13) J) / (1.673 × 10^(-27) kg)
v^2 ≈ 7.17 × 10^14 m^2/s^2
Taking the square root of both sides gives:
v ≈ √(7.17 × 10^14) m/s
v ≈ 2.68 × 10^7 m/s
3. Calculate the magnitude of the magnetic force (F):
Now, substitute the known values into the formula for magnetic force:
F = q * v * B * sin(θ)
Since the proton carries a charge of +1.60 × 10^(-19) C, the angle between the velocity vector and the magnetic field vector is 90 degrees because the proton is moving vertically downward and the magnetic field is pointing north.
F = (1.60 × 10^(-19) C) * (2.68 × 10^7 m/s) * (3.5 T) * sin(90 degrees)
F = 1.48 × 10^(-11) N
The magnetic force acting on the proton is approximately 1.48 × 10^(-11) N, directed to the east.
It seems that the numerical discrepancy in your answer may have resulted from a rounding error or an incorrect value used during the calculation. Make sure to double-check your calculations and use the correct values for each parameter to obtain the accurate result.