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Advanced Physics
Consider the specific example of a positive charge qqq 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., i^i^i_unit- j^j^j_unit). (Recall that i^i^i_unit is written \hat i (or alternatively i_unit can be used.))

Consider the specific example of a positive charge qqq 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., i^i^i_unit- j^j^j_unit). (Recall that i^i^i_unit is written \hat i (or alternatively i_unit can be used.))

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Part A)
Consider the specific example of a positive charge qqq 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., i^i^i_unit- j^j^j_unit). (Recall that i^i^i_unit is written \hat i (or alternatively i_unit can be used.))
 
Part B)
Now consider the example of a positive charge qqq 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.
 
Part C)
Now consider the example of a positive charge qqq moving in the xy plane with velocity v⃗ =vcos(θ)i^+vsin(θ)j^(i.e., with magnitude v at angle θ 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?
Express the direction of the force in terms of θ, as a linear combination of unit vectors, i^, j^, and k^.
 
Part D)
Now consider the case in which the positive charge qqq is moving in the yz plane with a speed v at an angle θ with the z axis as shown (Figure 2)(with the magnetic field still in the +z direction with magnitude B). Find the magnetic force F→ on the charge.
Express the magnetic force in terms of given variables like q, v, B, θ, and unit vectors.
The image depicts a three-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\). - The \(x\)-axis is oriented towards the bottom right. - The \(y\)-axis is oriented towards the right. - The \(z\)-axis is oriented upwards. There is a vector \(\vec{v}\) shown in green, originating from the origin, pointing diagonally, making an angle \(\theta\) with the vector \(\vec{B}\). The vector \(\vec{B}\) is represented by blue arrows and is aligned along the positive \(z\)-axis, indicating a magnetic field or a force field directed upwards. The angle \(\theta\) is the angle between the vectors \(\vec{v}\) and \(\vec{B}\). This diagram is often used to illustrate concepts such as the force exerted on a charged particle moving in a magnetic field, where the direction of the vectors and the angle between them are significant for understanding the relevant physics equations.
Transcribed Image Text:The image depicts a three-dimensional coordinate system with axes labeled \(x\), \(y\), and \(z\). - The \(x\)-axis is oriented towards the bottom right. - The \(y\)-axis is oriented towards the right. - The \(z\)-axis is oriented upwards. There is a vector \(\vec{v}\) shown in green, originating from the origin, pointing diagonally, making an angle \(\theta\) with the vector \(\vec{B}\). The vector \(\vec{B}\) is represented by blue arrows and is aligned along the positive \(z\)-axis, indicating a magnetic field or a force field directed upwards. The angle \(\theta\) is the angle between the vectors \(\vec{v}\) and \(\vec{B}\). This diagram is often used to illustrate concepts such as the force exerted on a charged particle moving in a magnetic field, where the direction of the vectors and the angle between them are significant for understanding the relevant physics equations.
**Figure: Three Right-Handed Coordinate Systems** The image illustrates three different configurations of right-handed coordinate systems, each defined by three perpendicular axes: x, y, and z. 1. **First System (Leftmost):** - The x-axis points horizontally to the right. - The y-axis points vertically upward. - The z-axis points forward, out of the plane of the page. 2. **Second System (Middle):** - The x-axis points horizontally to the right. - The y-axis points downward and slightly towards the viewer. - The z-axis points upward and slightly towards the viewer. 3. **Third System (Rightmost):** - The x-axis points horizontally to the left. - The y-axis points horizontally to the right. - The z-axis points vertically upward. Each representation maintains the right-hand orientation, meaning that curling the fingers of your right hand from x to y results in your thumb pointing along the z-axis.
Transcribed Image Text:**Figure: Three Right-Handed Coordinate Systems** The image illustrates three different configurations of right-handed coordinate systems, each defined by three perpendicular axes: x, y, and z. 1. **First System (Leftmost):** - The x-axis points horizontally to the right. - The y-axis points vertically upward. - The z-axis points forward, out of the plane of the page. 2. **Second System (Middle):** - The x-axis points horizontally to the right. - The y-axis points downward and slightly towards the viewer. - The z-axis points upward and slightly towards the viewer. 3. **Third System (Rightmost):** - The x-axis points horizontally to the left. - The y-axis points horizontally to the right. - The z-axis points vertically upward. Each representation maintains the right-hand orientation, meaning that curling the fingers of your right hand from x to y results in your thumb pointing along the z-axis.
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