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To find the potential difference due to a point charge, we can use the formula for electric potential ( V ) due to a point charge ( Q ):
[
V = frac{k cdot Q}{r}
]
where ( k ) is Coulomb’s constant (( k approx 8.99 times 10^9 , text{N m}^2/text{C}^2 )), ( Q ) is the charge, and ( r ) is the distance from the charge to the point where the potential is being calculated.
1. Location of the charge: ( (2, 3, 3) ) m
2. Charge ( Q ): ( 0.4 , text{nC} = 0.4 times 10^{-9} , text{C} )
3. Location A (where we calculate the potential): ( (2, 3, 3) ) m (same as the charge location)
4. Location B: ( (-2, 3, 3) ) m
### Step 1: Calculate potential at Point A
For point A, the distance ( r_A ) from the charge is 0, since it is located at the same point as the charge.
[
V_A = frac{k cdot Q}{r_A} quad
Answer: c
Explanation: Vab = (Q/4πεo)(1/rA) + (1/rB), where rA and rB are position vectors rA =1m and rB = 4m. Thus Vab = 2.7 volts.