Two long, straight wires, one above the other, are seperated by a distance d = 1.53 cm and are parallel to the x−axisx−axis. Let the +y−axis

Question

Two long, straight wires, one above the other, are seperated by a distance d = 1.53 cm and are parallel to the x−axisx−axis. Let the +y−axis+y−axis be in the plane of the wires in the direction from the lower wire to the upper wire. Each wire carries current 34 A in the +x−direction+x−direction. Find the magnetic force on a negative point charge 79 μCμC moving with velocity 3.49×105 m/s in the +y-direction, when the charge is:

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Nho 5 years 2021-07-18T07:10:32+00:00 1 Answers 35 views 0

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  1. King
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    2021-07-18T07:12:29+00:00
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    Answer:

    a)   F_x = F_y = F_x = 0 \ \ N

    b)  F_x= - 0.05718 \ N ; F_y = 0 \ N ; F_z= 0 \ N

    Explanation:

    Given that:

    q = -79 μC

    q = – 79×10⁻⁶ C

    d = 1.53 cm

    d = 0.0153 m

    I = 34 A

    v = 3.49×10⁵ m/s

    \bar{V} = v \hat{j}

    The force on charge q is given by

    \bar{ F } = q (\bar {v} * \bar{B})

    a) At midway (A) , the B will be :

    \bar{B} =\bar{B_1} + \bar{B_2}

    B_1  and  B_2 will be equally the same in respect to their magnitude but opposite direction at point A.

    So; \bar{|B_1|} = |B_2| = \frac{\mu_oI}{2 \pi d/2}

    where |B| =0

    ∴  \bar {|F|} = 0

    ∴ F_x = F_y = F_x = 0 \ \ N

    b)

    At a distance d/2 cm above the upper wire:

    \bar{B} =\bar{B_1} + \bar{B_2}

    where:

    B_1 =B_2 = \frac{\mu_o I }{2 \pi ( d + d/2 )}   ; upward to the plane of paper

    ∴ \frac{\mu_o I}{2 \pi} \ \ [\frac{2}{3/d} +\frac{2}{d}] \ \ \hat{k}

    B = \frac{\mu_o I}{ \pi \ d} \ \ [\frac{1}{3} +1] \ \ \hat{k}

    B = \frac{\mu_o I}{ \pi \ d} \ [\frac{4}{3} ] \ \hat{k}

    B = \frac{7 \pi * 10^{-7} *34}{\pi*0.0153}*\frac{4}{3} \ \hat{k}

    B = 2.074 × 10⁻³T  \hat {k}

    ∴ \bar {F} = q ( \bar{v} + \bar {B})

    \bar {F} = q ( \bar{v} + B)j*k\\\\\bar {F} = q ( \bar{v} + B) \bar {i}

    F = -79*10^{-6}*3.49*10^5*2.074*10^{-3}

    F = - 0.05718 \ N \ \hat {i}

    F_x= - 0.05718 \ N ; F_y = 0 \ N ; F_z= 0 \ N

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