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Electrostatics question

2024 · Q187
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Electrostatics question

2024 · Q187

NEETPhysicsElectrostaticsMCQ+4 / −1

The value of electric potential at a distance of 9 cm9 \mathrm{~cm}9 cm from the point charge 4×10−7C4 \times 10^{-7} \mathrm{C}4×10−7C is [Given 14πε0=9×109 N m2C−2\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 \mathrm{C}^{-2}4πε0​1​=9×109 N m2C−2] :

  1. A
    4×102 V4 \times 10^2 \mathrm{~V}4×102 V
  2. B
    44.4 V44.4 \mathrm{~V}44.4 V
  3. C
    4.4×105 V4.4 \times 10^5 \mathrm{~V}4.4×105 V
  4. D
    4×104 V4 \times 10^4 \mathrm{~V}4×104 V
View written solutionFree

Correct answer: D

The electric potential (V) at a distance (r) from a point charge (q) is given by:

$$V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$$

where $$\frac{1}{4 \pi \varepsilon_0}$$ is Coulomb's constant.

In this case, we have:

  • $$q = 4 \times 10^{-7} \mathrm{C}$$
  • $$r = 9 \mathrm{~cm} = 0.09 \mathrm{~m}$$
  • $$\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 \mathrm{C}^{-2}$$

Substituting these values into the equation for electric potential, we get:

$$V = (9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 \mathrm{C}^{-2}) \frac{(4 \times 10^{-7} \mathrm{C})}{(0.09 \mathrm{~m})}$$

$$V = 4 \times 10^4 \mathrm{~V}$$

Therefore, the value of electric potential at a distance of $9 \mathrm{~cm}$ from the point charge $$4 \times 10^{-7} \mathrm{C}$$ is $$4 \times 10^4 \mathrm{~V}$$.

The correct answer is Option D.

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