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The figure below shows point charges (+44.4 and -22.2)μC placed at corners of the square of sides 0.5m as shown below. Calculate electric Potential at S. Potential energy of the 10μC charge placed at S.

Physics

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2 parts
a

399.156 kV\text{399.156 kV}

b

3991.56 J\text{3991.56 J}

Step-by-step solution

3 steps

Ili kukokotoa uwezo wa umeme (electric potential) kwenye S na nishati ya uwezo (potential energy) ya chaji iliyowekwa kwenye S, tutatumia fomula za uwezo wa umeme unaosababishwa na chaji ya nukta.

Kutoka kwenye mchoro na maelezo:

  • Upande wa mraba, a=0.5 ma = 0.5 \, \text{m}
  • Chaji kwenye P, QP=−22.2 μC=−22.2×10−6 CQ_P = -22.2 \, \mu C = -22.2 \times 10^{-6} \, C
  • Chaji kwenye R, QR=+44.4 μC=+44.4×10−6 CQ_R = +44.4 \, \mu C = +44.4 \times 10^{-6} \, C
  • Kiwango cha Coulomb, k=8.99×109 N m2/C2k = 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2

Umbali kutoka S hadi P (rPSr_{PS}) ni urefu wa upande wa mraba, hivyo rPS=0.5 mr_{PS} = 0.5 \, \text{m}.
Umbali kutoka S hadi R (rRSr_{RS}) pia ni urefu wa upande wa mraba, hivyo rRS=0.5 mr_{RS} = 0.5 \, \text{m}.
Uwezo wa umeme kwenye S (VSV_S) ni jumla ya uwezo unaosababishwa na chaji QPQ_P na QRQ_R.

Part a· 2 steps

Kokotoa Uwezo wa Umeme kwenye S

  1. Tumia fomula ya uwezo wa umeme kwa chaji ya nukta, V=kqrV = \frac{kq}{r}.

    Uwezo wa jumla kwenye S ni VS=kQPrPS+kQRrRSV_S = \frac{kQ_P}{r_{PS}} + \frac{kQ_R}{r_{RS}}.

    VS=(8.99×109 N m2/C2)(−22.2×10−6 C0.5 m++44.4×10−6 C0.5 m)V_S = (8.99 \times 10^9 \, \text{N m}^2/\text{C}^2) \left( \frac{-22.2 \times 10^{-6} \, C}{0.5 \, \text{m}} + \frac{+44.4 \times 10^{-6} \, C}{0.5 \, \text{m}} \right)
  2. Rahisisha hesabu.

    VS=(8.99×109)((−22.2+44.4)×10−60.5) VV_S = (8.99 \times 10^9) \left( \frac{(-22.2 + 44.4) \times 10^{-6}}{0.5} \right) \, \text{V} VS=(8.99×109)(22.2×10−60.5) VV_S = (8.99 \times 10^9) \left( \frac{22.2 \times 10^{-6}}{0.5} \right) \, \text{V} VS=(8.99×109)(44.4×10−6) VV_S = (8.99 \times 10^9) (44.4 \times 10^{-6}) \, \text{V} VS=399.156×103 VV_S = 399.156 \times 10^3 \, \text{V} VS=399.156 kVV_S = 399.156 \, \text{kV}

    Uwezo wa umeme kwenye S ni 399.156 kV\boxed{\text{399.156 kV}}.

Part b

3991.56 J\text{3991.56 J}

Nishati ya Uwezo ya Chaji ya 10 mC Iliyowekwa kwenye S

  1. Tumia fomula ya nishati ya uwezo, U=q′VU = q'V, ambapo q′q' ni chaji iliyowekwa na VV ni uwezo kwenye eneo hilo.

    Chaji iliyowekwa kwenye S, q′=10 mC=10×10−3 C=1×10−2 Cq' = 10 \, \text{mC} = 10 \times 10^{-3} \, C = 1 \times 10^{-2} \, C.
    Uwezo kwenye S, VS=399.156×103 VV_S = 399.156 \times 10^3 \, \text{V}.

    US=q′VSU_S = q' V_S US=(1×10−2 C)×(399.156×103 V)U_S = (1 \times 10^{-2} \, C) \times (399.156 \times 10^3 \, \text{V}) US=3991.56 JU_S = 3991.56 \, \text{J}

    Nishati ya uwezo ya chaji ya 10 mC iliyowekwa kwenye S ni 3991.56 J\boxed{\text{3991.56 J}}.

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