What minimum magnetic field is necessary to exert a 15 Newton force on a 175 milliCoulomb charge moving at 250 meters/secon through the field?
To determine the minimum magnetic field necessary to exert a force on a moving charged particle, you can use the following formula:
F = |q| * v * B * sin(θ)
Where:
F is the force
|q| is the magnitude of the charge
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, which we assume to be 90 degrees for maximum force
From the given information:
Charge, q = 175 milliCoulomb (175 x 10^-3 Coulomb)
Velocity, v = 250 meters/second
Force, F = 15 Newtons
θ = 90 degrees
Plugging in these values into the formula, we get:
15 Newtons = |175 x 10^-3 Coulomb| * 250 m/s * B * sin(90 degrees)
Since sin(90 degrees) is equal to 1, we can simplify the equation to:
15 Newtons = 175 x 10^-3 Coulomb * 250 m/s * B
Now, solve for B:
B = 15 N / (175 x 10^-3 C * 250 m/s)
B = 0.343 T (Tesla)
So, the minimum magnetic field necessary to exert a 15 Newton force on a 175 milliCoulomb charge moving at 250 meters/second through the field is approximately 0.343 Tesla.