27. Magnetic Field and Magnetic Forces

27. Magnetic Field and Magnetic Forces - [ Problem View ]...

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[ Problem View ] Force on Moving Charges in a Magnetic Field Description: Student goes through right-hand rule questions and then looks at force on a charge moving at particular velocity through uniform magnetic field. Learning Goal: To understand the force on a charge moving in a magnetic field. 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 as the interaction of that magnet with the magnetic field at its location (the field being generated by other magnets or currents). More fundamentally, the force 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 can be negative), is its velocity, and is the local magnetic field. This force is nonintuitive, as it involves the vector product (or cross product) of the vectors and . In the following questions we assume that the coordinate system being used has the conventional arrangement of the axes, such that it satisfies , where , , and are the unit vectors along the respective axes. Let's go through the right-hand rule. Starting with the generic vector cross-product equation point your forefinger of your right hand in the direction of , and
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point your middle finger in the direction of . Your thumb will then be pointing in the direction of . Part A Consider the specific example of a positive charge moving in the + x direction with the local magnetic field in the + y direction. In which direction is the magnetic force acting on the particle? Express your answer using unit vectors (e.g., - ). (Recall that is written x_unit .) ANSWER: Direction of = z_unit Part B Now consider the example of a positive charge moving in the + x direction with the local magnetic field in the + z direction. In which direction is the magnetic force acting on the particle? Express your answer using unit vectors. ANSWER: Direction of = -y_unit
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Part C Now consider the example of a positive charge moving in the xy plane with velocity (i.e., at angle with respect to the x axis). If the local magnetic field is in the + z direction, what is the direction of the magnetic force acting on the particle? Hint C.1 Finding the cross product The direction can be found by any of the usual means of finding the cross product: 1. Use the determinant expression for the cross product. (See your math or physics text.) 2. Use the general definition , where any term with the three directions in the normal order of xyz or any cyclical permutation (e.g., yzx or zxy ) has a positive sign, and terms with the other order ( xzy , zyx , or yxz ) have a negative sign. Express the direction of the force in terms of
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27. Magnetic Field and Magnetic Forces - [ Problem View ]...

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