A 2.0 c charge moves with a velocity of (2.0i+4.0j+6.0k)m/s and experiences a magnatic force of (0.4i-20j+12k)N. The x component of the magnatic field is equal to zero. Determine the y component of the magnatic field

Explanation:

Here we can use the Lorentz force equation.

We know:

So we will have:

Let's solve the cross product, knowing that x component of B is 0, it means a=0.

Comparing the k component we have:

If we see b is the y-component of the magnetic field, therefore

I hope it helps you!

-0.033 units

According to Lorentz force law, the magnetic force, F, on a moving charge, q, moving with a velocity, v, in a magnetic field, B, is given by;

F = q v x B   ----------------(i)

Where;

F, v and B are vectors. Therefore, equation (i) represents a vector product of the velocity and magnetic field vectors.

From the question;

v = (2.0i + 4.0j + 6.0k)m/s

F = (0.4i - 20j + 12k)N

q = 2.0C

Let the magnetic field vector be given by;

B = ai + bj + ck               ---------------------(*)

Where;

a, b and c are the magnitudes of the x, y and z components of the magnetic field.

Substitute the values of F, v, B and q into equation (i) as follows;

(0.4i - 20j + 12k) = 2.0(2.0i + 4.0j + 6.0k) x (ai + bj + ck)

Expanding the second bracket gives

(0.4i - 20j + 12k) = (4.0i + 8.0j + 12.0k) x (ai + bj + ck)          ---------------(ii)

Solving the right hand side of equation (ii) which is the vector product gives;

                                       |                                       |

                                       |  i               j                 k |

 (0.4i - 20j + 12k) =        |  4.0         8.0         12.0  |

                                      |  a             b                 c  |

                                      |                                        |

(0.4i - 20j + 12k)  = (8.0c - 12.0b)i - (4.0c -12.0a)j + (4.0b - 8.0a)k      ----(iii)

Comparing both sides of equation (iii) gives the following three equations;

0.4 = 8.0a - 12.0b           --------------------(iv)

-20 = 4.0c - 12.0a          ---------------------(v)

12 = 4.0b - 8.0a             ----------------------(vi)

From the question, it is given that the x component of the magnetic field is equal to zero. Now, recall that from equation (*) above, the magnitude of the x-component of the magnetic field is given as a

Therefore;

a = 0

To get the y component, which is b, substitute the value of a = 0 into equation (iv) as follows;

0.4 = 8.0(0) - 12.0b

0.4 = 0 - 12.0b

0.4 = - 12.0b

Solve for b;

b = = -0.033

Therefore the y component of the magnetic field is -0.033 units

true tan speed = ang vel x radius

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