The force on a charged particle moving in a magnetic field can be computed as the vector sum of the forces due to each separate component of the magnetic field. As an example, a particle with charge q is moving with speed v in the? y-direction. It is moving in a uniform magnetic field
Part A
What is the x-component of the force F? exerted on the particle by the magnetic field?
Part B
What is the y-component of the force F? exerted on the particle by the magnetic field?
Part C
What is the z-component of the force F? exerted on the particle by the magnetic field?
Part D
If q<0 and Bx=By=Bz>0, find the magnitude of F? in terms of q, v, and Bx.
Part E
If q<0 and B_xvq=B_yvq=B_zvq=1, find the direction of F
Express your answer in terms of unit vectors i, j, and k.
The concepts required to solve the problem are the magnetic force due to particle moving in magnetic field, the vector product and the direction and magnitude of the vectors.
Initially, use the charge, velocity vector and the magnetic field to calculate the magnetic force. Later on, choose the components of the field in each direction and finally use the components to calculate the magnitude and direction of the force.
The magnetic force acting on a charge moving in a magnetic field is,
Here, is the force, is the charge of the particle, is the speed, and is the magnetic field.
The force, velocity and the magnetic field are vectors. The vectors have both direction and magnitude.
The force can be represented in vector form as,
Here, is the x component of the force, is the y component of the force, is the z component of the force. , and are unit vectors along x, y and z axis.
The velocity can be represented in vector form as,
Here, is the x component of the velocity, is the y component of the velocity, is the z component of the velocity. , and are unit vectors along x, y and z axis.
The magnetic field can be represented in vector form as,
Here, is the x component of the magnetic field, is the y component of the magnetic field, is the z component of the magnetic field. , and are unit vectors along x, y and z axis.
The cross product of the velocity vector and the magnetic field is,
The cross product of magnetic force is,
The x component of the magnetic force is,
The y component of the magnetic force is,
The z component of the magnetic force is,
The magnitude of the force is,
(A)
The x component of the magnetic force acting on the particle is,
Substitute for and for . The x component of the magnetic force is,
The x component of the magnetic force acting on the particle is .
(B)
The y component of the magnetic force acting on the particle is,
Substitute for and for . The y component of the magnetic force is,
The y component of the magnetic force acting on the particle is .
(C)
The z component of the magnetic force acting on the particle is,
Substitute for and for . The z component of the magnetic force is,
The z component of the magnetic force acting on the particle is .
(D)
The magnitude of the force is,
Substitute for , for and for . The magnitude of magnetic force is,
For a charge,
Substitute for in to find the magnitude of magnetic force.
The magnitude of magnetic force is,
(E)
The force can be represented in vector form as,
Substitute for , for and for . The magnetic force is,
For , .
Substitute 1 for and 1 for in to find the direction of magnetic force.
Ans: Part AThe x component of the magnetic force acting on the particle by the magnetic field is .
Part BThe y component of the magnetic force acting on the particle by the magnetic field is .
Part CThe z component of the magnetic force acting on the particle by the magnetic field is.
Part DThe magnitude of the magnetic force is .
Part EThe direction of magnetic force is .
The force on a charged particle moving in a magnetic field can be computed as the...
Magnets exert forces on other magnets even though they are separated by some distance. Usually the force on a magnet (or piece of magnetized matter) is pictured asthe interaction of that magnet with the magnetic field at its location (the field being generated by other magnets or currents). More fundamentally, theforce arises from the interaction of individual moving charges within a magnet with the local magnetic field. This force is written ,where is the force, is the individual charge (which...
2) The force that a magnetic field exerts on a charged particle is given by Ę = qö xĒ. A particle with mass m= 2.0x108 kg and charge q = +2.5x10-8C has an initial speed of v = 4+2 x 103 m/s (in the x- y plane). The magnetic field vector and velocity vector are B and û, respectively are displayed on the coordinate axis below. The angle between the vectors is 135 degrees. Use unit vector notation when describing...
2) The force that a magnetic field exerts on a charged particle is given by F = qö x B. A particle with mass m = 2.0x10 kg and charge q - +2.5x10°C has an initial speed of v = 4/2 x 103 m/s (in the x- y plane). The magnetic field vector and velocity vector are 5 and 0, respectively are displayed on the coordinate axis below. The angle between the vectors is 135 degrees. Use unit vector notation...
[1 point] A negatively charged particle has a velocity in the negative z-direction at point P. The magnetic force on the particle at this point is in the negative y-direction. Which of the following statements about the magnetic field at point P can be determined from this data? [Notation: "B"represents the magnitude of the component of the magnetic field in the i-tih direction.] 1.) What information can be deduced about B,? a. Br is negative. b. B is positive. c....
The direction of the magnetic force on a moving charged particle in a magnetic field is __________. A.perpendicular to the magnetic field B.perpendicular to the velocity C. both perpendicular to the velocity and perpendicular to the magnetic field
27A - Magnetic Fields and Forces 1) The force that a magnetic field exerts on a charged particle is given by È = qö x B. Assume charge q=+1.5 nC, B = 0.30 T and 0 = 25 m/s. The directions of the magnetic field vector and velocity vector are ] and , respectively are displayed on the coordinate axis below. The angle between the vectors is 90, degrees. Use unit vector notation when describing the vectors. z (0, 0,...
3) A charged particle is moving with velocity of V in a magnetic field of B, which one of the followings is correct: A) The direction of force F on the charge is parallel to magnetic field B B) The direction of force F on the charge is parallel to velocity direction V C) The force is maximized when velocity direction and magnetic field are parallel D) The force F is perpendicular (normal) to both velocity V and magnetic field...
A uniform magnetic field is in the positive z direction. A positively charged particle is moving in the positive x direction through the field. The net force on the particle can be made zero by applying an electric field in what direction?
Motion in a Magnetic Field 1 1 2 3 4 5 6 A charged particle of mass m = 5.9X10-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 2.8T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.83 m, 0) and leaves the region at (x,y) = 0, 0.83 m a time t = 619 μs after it entered the region. 1) With...
A particle with a charge of q = -5.68nC is moving in a uniform magnetic field of B? =( 2.20T ) z^. The magnetic force on the particle is measured to beF? =( 6.10?N )?y^. a) Calculate the x component of the velocity of the particle. b)What is the radius of the circular motion the particle will have in the magnetic field if the particle has a mass of 0.700g ? c)What is the period of this circular motion? d)What...