Question

Find the direction of the magnetic field B acting on a moving proton shown in the figure below if the direction of the magnetic force acting on it is as indicated. Assume that the magnetic field B acting on this proton is perpendicular to the velocity of this proton at the moment depicted in this figure. (As a standard convention, the symbol denotes a vector pointing into the page, and the symbol o denotes a vector pointing out of the page.) (in) For this problem (Hint: In this case, the magnetic field B is unknown. Use the right-hand palm rule to determine the direction of the magnetic field B do NOT use the right-hand rule for the cross product because it's harder to be applied to this problem.) What is the direction of the magnetic field B acting on this proton at the moment depicted in this figure ? The magnetic field points: A to the right: B. out of the page: C. into the page

Answer 1

The expression for magnetic force $(\vec{F})$ acting on a charged partical carrying charge moving with velocity $(\vec{v})$ in magnetic field
(B
is given as,

$\vec{F}=q(\vec{v}\times\vec{B})$

So we see that the magnetic force $\vec{F}$ is directed the same direction of vector $\vec{v}\times\vec{B}$ if charge is positive or in the opposite direction of vector $\vec{v}\times\vec{B}$ if the charge is negative.

Note that vector $\vec{v}\times\vec{B}$ is directed perpendicular to plane containing both vectors $\vec{v}$ and $\vec{B}$ .

This implies force $\vec{F}$ is also directed perpendicular to plane containing both vectors $\vec{v}$ and $\vec{B}$ .

In our case we have we have a proton moving in magnetic field,

Since proton carries positive charge, the magnetic force $(\vec{F}=\vec{F_{B}})$ acting on proton will be directed in the same direction of vector $(\vec{v}\times\vec{B})$

direction of magnetic force $\vec{F_{B}}$ acting on proton can be found by using right hand palm rule as,

stretch all the fingers of right hand in a single direction and stretch the thumb outward such that the thumb of right hand points in the direction perpendicular to direction of right hand fingers and also note that all the fingers and thumb of right hand must lie in the same plane,

Now holding right hand in this confuration if we point the thumb in the direction on velocity $\vec{v}$ of proton and hold our palm such that force $\vec{F_{B}}$ is directed perpendicularly outward of the right hand palm, then the strecthed fingers will point in the direction of magnetic field $\vec{B}$ .

Below I have drawn the direction of magnetic field $\vec{B}$ found using above mentioned right hand rule given the directions of force $\vec{F_{B}}$ and velocity $\vec{v}$ of proton.

܀ fe
so as we see above the correct answer is magnetic field $\vec{B}$ is directed to the right .