One component of a magnetic field has a magnitude of 0.048 T and points along the +x axis, while

One component of a magnetic field has a magnitude of 0.048 T...

One component of a magnetic field has a magnitude of $0.048 \mathrm{T}$ and points along the $+x$ axis, while the other component has a magnitude of $0.065 \mathrm{T}$ and points along the $-y$ axis. A particle carrying a charge of $+2.0 \times 10^{-5} \mathrm{C}$ is moving along the $+z$ axis at a speed of $4.2 \times 10^{3} \mathrm{m} / \mathrm{s} .$ (a) Find the magnitude of the net magnetic force that acts on the particle. (b) Determine the angle that the net force makes with respect to the $+x$ axis.

Transcript

00:01 This question we are given here magnetic force f which is equal we can write you here q multiplied by v cross b now let's take a magnitude so maybe here if you want to find a magnitude so we can write f which is equal to qab here sign theorem now in this question we are given a value of q here value of q we are given here 2 multiplied by 10 x2 minus 5 column now magnetic field we are given here that 0 .08 0 0 08 i.

00:33 Here minus we can write 0 .06 here 0 .06 sthcla is in the j karat.

00:41 So i .krat and j now velocity we are given here 4 .2 multiple by 10 ratio 3 10 ratio 3 meter per second k karat now here let's write find out v cross v which is equal we can write here the first vector this row here so let's put here taking the cross product so let's find out the cross product so here we can write i j and k here 0 0 4 .2 multiple of a 103 2 3 here we can write 0 .0 4 8 here we can write 0 .0 6 5 and 0 now we just simplify and we can write here answer is so v which is equal to answer is 273 here tesla i karat plus we can write 201 1 .6 tesla here right jkarrate and unit here is tesla meter per second so this is the value of v gross v now let's find out the magnetic here magnitude of magnetic force so here we can write magnitude of magnetic force f is equal to we know the mass here we have charged 2 multiple 10 to minus 5 here we can write 273 here i here we can write i cared plus we can write 201 .6 here j karat now we just simply find we can write here the answer is 5 .46 1 by 10 to minus 3 here we can write 10 minus 3 i karat plus we can write 4 .03 by 10 .0 .3 minus 3 here j so this is the value of force here.

02:30 This is the value of here we can write force.

02:33 Now let's find out this magnitude.

02:35 So here we can write magnitude of f...

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