There is a 0.225 T magnetic field directed along the +x axis and a field of unknown magnitude along the +y axis. A particle carrying a charge of 7.20 10-5 C experiences a maximum force of 0.455 N when traveling at a speed of 2 104 m/s through the region where the fields are. Find the magnitude of the unknown field.

Question

There is a 0.225 T magnetic field directed along the +x axis and a field of unknown magnitude along the +y axis. A particle carrying a charge of 7.20 10-5 C experiences a maximum force of 0.455 N when traveling at a speed of 2 104 m/s through the region where the fields are. Find the magnitude of the unknown field.

Answer 1

Do you mean V = 2*10^4 ???

F = q ( V x B )
the force is maximum when the velocity vector is perpendicular to the B fieldso consider the B field in the x y plane and V in the z direction.
then
|F| = |q| |V| |B|
so
.455 = 7.210^-5 * 2 * 10^4 * |B|
|B| = .316 T
so
Bx^2 + By^2 = |B|^2 = 0.1 T
.225^2 + By^2 = .1
.05 + By^2 = .1
so By is also about .22 T

Answer 2

where did you get .1 from?

Answer 3

The .1 is from |B|^2 which is equal to .316^2

Answer 4

To find the magnitude of the unknown field, we can use the formula for the magnetic force experienced by a charged particle in a magnetic field. The formula is:

F = q * v * B

Where:
F is the force experienced by the particle,
q is the charge of the particle,
v is the velocity of the particle, and
B is the magnetic field.

In this case, we are given:
F = 0.455 N
q = 7.20 * 10^-5 C
v = 2 * 10^4 m/s
Bx = 0.225 T (magnetic field along +x axis)

Now, the force experienced by the particle is given as the maximum force. This indicates that the particle is moving in a direction perpendicular to the magnetic field, which means the force experienced is due to the magnetic field along the +y axis.

Now, let's break down the force into its x and y components:

Fx = q * vx * Bx (In this case, the particle is not experiencing any force along the x-axis, so Fx = 0)
Fy = q * vy * By (This is the force experienced along the y-axis)

Now, we know that Fy = F = 0.455 N.

Plugging in the values, we get:

0.455 N = (7.20 * 10^-5 C) * (2 * 10^4 m/s) * By

Simplifying the equation, we have:

0.455 N = 1.44 C * 10^5 m/s * By

Now, we can solve for By:

By = 0.455 N / (1.44 C * 10^5 m/s)

Simplifying further, we get:

By = 0.455 N / 1.44 C * 10^5 m/s

By = 3.16 * 10^-6 T

Therefore, the magnitude of the unknown field along the +y axis is 3.16 * 10^-6 T.