Magnetic field of a point charge + example of magnetic force between two charges.
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4 ماه پیش
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We work out a formula
We work out a formula for the magnetic field of a point charge, noting that this formula is actually a low-velocity approximation, then we work an example of magnetic force between two charges.
First, we examine a positive charge q moving at speed v, and we select an observation point at which to measure the magnetic field of a moving charge. We draw a position vector, making an angle of theta with the velocity axis, and we note that B should be proportional to both q and v. Next, we note the angular dependence of magnetic field: the magnetic field is zero in the direction of velocity and maximized perpendicular to the velocity. Next, we define a unit vector r-hat pointing in the direction of the position vector r, and we establish that a cross product of v and r-hat is a great way to capture the proportionality to both v and sin(theta) in addition to giving the correct direction for the looping magnetic field lines around the direction of velocity. We put it all together and get a formula for magnetic field of a moving charge: B=mu_0/4pi*qvXr-hat/r^2.
Next, we work an example, finding the magnetic force between two positive charges. We have two charges of +q each moving at a speed of v, and we compute the magnetic force between charges at the closest approach distance of r. We start by setting up the position vector and unit vector. We determine the direction of B and use the formula for magnetic field of point charges to determine the magnitude of B. Finally, we use the Lorentz force law F=qvXB to get the direction of magnetic force and the magnitude of the magnetic force on the second charge.
#physics #magnetism #apphysics
First, we examine a positive charge q moving at speed v, and we select an observation point at which to measure the magnetic field of a moving charge. We draw a position vector, making an angle of theta with the velocity axis, and we note that B should be proportional to both q and v. Next, we note the angular dependence of magnetic field: the magnetic field is zero in the direction of velocity and maximized perpendicular to the velocity. Next, we define a unit vector r-hat pointing in the direction of the position vector r, and we establish that a cross product of v and r-hat is a great way to capture the proportionality to both v and sin(theta) in addition to giving the correct direction for the looping magnetic field lines around the direction of velocity. We put it all together and get a formula for magnetic field of a moving charge: B=mu_0/4pi*qvXr-hat/r^2.
Next, we work an example, finding the magnetic force between two positive charges. We have two charges of +q each moving at a speed of v, and we compute the magnetic force between charges at the closest approach distance of r. We start by setting up the position vector and unit vector. We determine the direction of B and use the formula for magnetic field of point charges to determine the magnitude of B. Finally, we use the Lorentz force law F=qvXB to get the direction of magnetic force and the magnitude of the magnetic force on the second charge.
#physics #magnetism #apphysics
4 ماه پیش
در تاریخ 1403/02/14 منتشر شده
است.
376
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