A particle has a charge of q = +5.8 ?C and is located at the origin. As the draw

Question

A particle has a charge of q = +5.8 ?C and is located at the origin. As the drawing shows, an electric field of Ex = +234 N/Cexists along the +x axis. A magnetic field also exists, and its x and y components are Bx = +1.3 T and By = +1.6 T. Calculate the force (magnitude and direction) exerted on the particle by each of the three fields when it is (a) stationary, (b) moving along the +x axis at a speed of 345 m/s, and (c) moving along the +z axis at a speed of 345 m/s.

A particle has a charge of q = +5.8 ?C and is located at the origin. As the drawing shows, an electric field of Ex = +234 N/Cexists along the +x axis. A magnetic field also exists, and its x and y components are Bx = +1.3 T and By = +1.6 T. Calculate the force (magnitude and direction) exerted on the particle by each of the three fields when it is (a) stationary, (b) moving along the +x axis at a speed of 345 m/s, and (c) moving along the +z axis at a speed of 345 m/s.

Explanation / Answer

a) when stationary there is no force due to the magnetic field,
so F = E*q = 239*4.5x10^-6 = 1.08x10^-3N at 0o (along the + x axis)

b) The force form the electric doesn't change but the force from the magnetic field is q*v*B*sin(?)
. Only the y component of the field will create a force on a charge moving along the x axis

So FB = 4.5x10^-6*345*1.5 = 2.33x10^-3N in the +z direction

So F = sqrt((1.08x10^-3)^2 +(2.33x10^-3)^2) = 2.57x10^-3N .The direction is in the x-z plane at an angle of arctan(2.33x10^-3/1.08x10^-3) = 65.1o to the x axis

c) Again FE = 1.08x10^-3N;
The y component of the magnetic force = 4.5x10^-6*345*1.4 = 2.17x10^-3N
The x component of the magnetic force = 4.5x10^-6*345*1.5 = 2.33x10^-3N, but its direction is in the -x

So net force is Fx = 1.08x10^-3- 2.33x10^-3 = -1.25x10^-3N and
the y component Fy = 2.17x10^-3N

So F = sqrt((1.25x10^-3)^2 + (2.17x10^-3)^2) = 2.50x10^-3N and
the angle = arctan(2.17x10^-3/(-1.25x10^-3)) = -60.1o but since x is< 0 + 180
so ? = -60.1 + 180 = 120o

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