Question

A long, straight wire lies along the x-axis and carries current I=65.0 A in the +x-direction. A small particle with mass 4.00×10 −6kg and charge 8.00×10 −3C is traveling in the vicinity of the wire. At an instant when the particle is on the y-axis at y=9.00 cm, its acceleration has components a x =−5.00×10 3m/s 2and a y=+9.00×10 3 m/s 2

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Answer 1

To calculate the magnetic force on the segment of wire between x = 2.0 m and x = 4.0 m, we need to first calculate the magnetic field at those points using the given equation. Once we have the magnetic field, we can use the formula for the magnetic force on a current-carrying wire to calculate the force.

Step-by-step explanation:

To calculate the magnetic force on the segment of wire between x = 2.0 m and x = 4.0 m, we need to first calculate the magnetic field at those points. The magnetic field at any point is given by B = 2.01 + 5.0x²ĵ, where x is in meters and B is in millitesla. Plugging in the values for x, we can find the magnetic field at x = 2.0 m and x = 4.0 m. Once we have the magnetic field, we can use the formula for the magnetic force on a current-carrying wire, F = I * L * B, where I is the current, L is the length of the wire segment, and B is the magnetic field, to calculate the force. Plug in the given values and we can find the magnetic force on the wire segment.

Answer 2

The components of velocity are v_x = 0 + (-5.00 ×
`10^(3)` m/
`s^(2)`) * t and v_y = 0 + (9.00 ×
`10^(3)` m/
`s^(2)`) * t.

To calculate the x and y components of the velocity of the particle, you can use the equations of motion.

In order to calculate the x and y components of the velocity of the particle, we can use the equations of motion. The equation for the x-component of velocity is given by:

v_x = v_0x + a_xt

where v_0x is the initial x-component of velocity, a_x is the x-component of acceleration, and t is the time. Plugging in the values:

v_x = 0 + (-5.00 ×
`10^(3)` m/
`s^(2)`) * t

Similarly, the equation for the y-component of velocity is:

v_y = v_0y + a_yt

where v_0y is the initial y-component of velocity, a_y is the y-component of acceleration, and t is the time. Plugging in the values:

v_y = 0 + (9.00 ×
`10^(3)` m/
`s^(2)`) * t

The direction of the force is given by the right-hand rule, where you point your thumb in the direction of the velocity, your index finger in the direction of the magnetic field, and your middle finger will point in the direction of the force.