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6. (i) An electron travels along the x axis with a velocity v = (vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.

6. (i) An electron travels along the x axis with a velocity v = (vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.

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6. (i) An electron travels along the x axis with a velocity v = (Vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.
Transcribed Image Text:6. (i) An electron travels along the x axis with a velocity v = (Vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.
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6. (i) An electron travels along the x axis with a velocity v = (Vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.
Transcribed Image Text:6. (i) An electron travels along the x axis with a velocity v = (Vo,0,0). Its 3D coordinates are (0,0,0) when it enters a region of length L within which a constant and weak magnetic field of B = (0,Bo,0) is applied. The effect of the weak magnetic field is to cause a small deviation in the path of the electron so that it does not pass through the point (L,0,0) which it would do in the case of Bo = 0. Find an expression for the location (x,y,z) of the electron after it has travelled a distance L in the x direction. (ii) An energetic collision between a fast electron and an electron at rest is used to create an electron-positron pair. Show that for this to happen, the minimum amount of kinetic energy of the fast electron must be at least 6mec?, where me is the mass of the electron.
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