Points A and B lie within a region of space where there is a uniform electric field that has no x- or z-component; only the y-component Ey i

Question

Points A and B lie within a region of space where there is a uniform electric field that has no x- or z-component; only the y-component Ey is non zero. Point A is at y=8.00 cm and point B is at y=15.0 cm. The potential difference between B and A is VB−VA=+12.0 V, so point B is at higher potential than point A. (a) Is Ey positive or negative? (b) What is the magnitude of the electric field? (c) Point C has coordinates x=5.00 cm, y=5.00 cm. What is the potential difference between points B and C?

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Hải Đăng 5 years 2021-08-02T09:30:50+00:00 1 Answers 487 views 1

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  1. thaiduong
    0
    2021-08-02T09:32:41+00:00
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    Answer:

    (a) Ey is negative

    (b) The magnitude of the electric field is E = 171.429 V/m

    (c) The potential difference between points B and C is 17.1429 V

    Explanation:

    (a) Here, we have the potentials given by;

    V_A - V_B = +12.0V with point A at y = 8.00 cm and point B at point y = 15.0 cm

    where point B is at a higher potential than point A, that is the electric potential is from;

    B with y = 15.0 cm to A with y = 8.0 cm which means

    E_y decreases as y increases or E_y  is negative.

    (b) The magnitude of the electric field is given by

    The work done to move a charge from B to A is

    W_{BA} = - \Delta U where

    \Delta U = U_a -U_b = q_0E(y_b-y_a)

    V_{BA} = \frac{\Delta U}{q_0} = \frac{q_0E(y_b-y_a)}{q_0} = E(y_b-y_a)

    ∴ E = \frac{V_{BA}}{(y_b-y_a)}

    E = \frac{12 \hspace{0.09cm}V}{(0.015\hspace{0.09cm} m -0.008\hspace{0.09cm} m)}

    E = 171.429 V/m

    (c) Here we have point C x = 5.00 cm and y = 5.00 cm

    Therefore we have the distance from B to C given by

    y_b-y_c = 15.00 \hspace{0.09cm}cm - 5.00 \hspace{0.09cm}cm = 10.00 \hspace{0.09cm} cm

    Where 10.00 cm = 0.01 m

    E = V/Δy

    Therefore, V = Δy·E

    For V_{BC}, Δy = y_b-y_c = 0.01 \hspace{0.09cm} m and we have,

    V_{BC} = E\times (y_b-y_c)

    V_{BC} = 171.429\times (0.015-0.005) = 17.1429\hspace{0.09cm}V

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