Question

QUESTION 1:

A +73 nC charge is positioned 2 m from a +33 nC charge. What is the magnitude of the electric field at the midpoint of these charges, in units of N/C?

QUESTION 2;

Two identical +4 nC charges are separated by a distance of 21 mm.  What is the electric potential at the midpoint of the charges, in units of Volts?

QUESTION 3:

What is the magnitude of the change in electric potential in moving from a point 24 cm from a +0.006 C to a point 86 cm from the charge, in units of volts?

give your answer as a positive value

Answer 1

Answer 2

QUESTION 1: Electric Field at Midpoint

Given:

• $q_1=+73\text{nC}=73\times 10^{-9}\text{C}$

• $q_2=+33\text{nC}=33\times 10^{-9}\text{C}$

• Distance between charges $d=2\text{m}$ → Midpoint at $r=1\text{m}$ from each.

• 
  

Electric field due to each charge at midpoint ($E=k\frac{\mathrm{\mid }q\mathrm{\mid }}{r^2}$):

• $E_1=(9\times 10^9)\frac{73\times 10^{-9}}{1^2}=657\text{N/C}$ (points away from $q_1$)

• $E_2=(9\times 10^9)\frac{33\times 10^{-9}}{1^2}=297\text{N/C}$ (points away from $q_2$)

• 
  

Total field (opposite directions, subtract magnitudes):

$$E_{\text{net}}=E_1-E_2=657-297=360\text{N/C}$$

Answer: 360 N/C

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QUESTION 2: Electric Potential at Midpoint

Given:

• Two $+4\text{nC}$ charges, $d=21\text{mm}=0.021\text{m}$

• Midpoint distance $r=0.0105\text{m}$ from each.

Potential due to each charge ($V=k\frac{q}{r}$):

$$V_1=V_2=(9\times 10^9)\frac{4\times 10^{-9}}{0.0105}\approx 3428.57\text{V}$$

Total potential (add contributions):

$$V_{\text{total}}=2\times 3428.57\approx 6857\text{V}$$

Answer: 6860 V (rounded to 3 sig figs)

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QUESTION 3: Change in Electric Potential

Given:

• Charge $q=+0.006\text{C}$

• Initial distance $r_i=24\text{cm}=0.24\text{m}$

• Final distance $r_f=86\text{cm}=0.86\text{m}$

Potential difference ($\mathrm{\Delta }V=kq(\frac{1}{r_f}-\frac{1}{r_i})$):

$$\mathrm{\Delta }V=(9\times 10^9)(0.006)(\frac{1}{0.86}-\frac{1}{0.24})$$$$\mathrm{\Delta }V=5.4\times 10^7(1.163-4.167)=5.4\times 10^7(-3.004)\approx -1.622\times 10^8\text{V}$$

Magnitude: $\mathrm{\mid }\mathrm{\Delta }V\mathrm{\mid }=1.62\times 10^8\text{V}$

Answer: 1.6 × 10⁸ V (2 sig figs, positive value)