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QNEET-2024-Ph-165: NEET 2024 Physics - Class 12 NEET-2024-Ph-165 Solution: A metal cube of side 5 cm is charged with \(6 C\). The surface…

A metal cube of side 5 cm is charged with 6μC6\mu C. The surface charge density on the cube is 0.125×10−3 Cm−20.125 \times 10^{-3}\ \text{Cm}^{-2} 0.25×10−3 Cm−20.25 \times 10^{-3}\ \text{Cm}^{-2} 4×10−3 Cm−24 \times 10^{-3}\ \text{Cm}^{-2} 0.4×10−3 Cm−20.4 \times 10^{-3}\ \text{Cm}^{-2}

Multiple Choice Options

  • A 0.125×10−3Cm−20.125 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2} 0.125 _ 1 0 _ 3 C m _ 2
  • B 0.25×10−3Cm−20.25 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2} 0.25 _ 1 0 _ 3 C m _ 2
  • C 4×10−3Cm−24 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2} 4 _ 1 0 _ 3 C m _ 2
  • D 0.4×10−3Cm−20.4 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2} 0.4 _ 1 0 _ 3 C m _ 2

Step-by-Step Verified Solution

To find the surface charge density of a charged metal cube, we need to determine the charge per unit area. The surface charge density, denoted by _ , is given by: _ = Q A where: Q QQ Q is the total charge on the cube A AA A is the total surface area of the cube The cube has a side length of 5   c m 5 cm5 \mathrm{~cm} 5   cm , so each side of the cube is 5   c m 5 cm5 \mathrm{~cm} 5   cm . Since 1 cm = 0.01 m, the side length in meters is: 5   cm = 0.05   m The cube has 6 faces, and the area of one face is given by: Area of one face = ( 0.05   m ) 2 = 0.0025   m 2 Therefore, the total surface area of the cube is: A = 6 _ 0.0025   m 2 = 0.015   m 2 The total charge, Q QQ Q , is given as 6 _ C 6μC6 \mu \mathrm{C} 6 _ C . Converting this to Coulombs: 6 _ C = 6 _ 10 _ 6   C Now, plugging the values into the formula for surface charge density: _ = 6 _ 10 _ 6   C 0.015   m 2 = 4 _ 10 _ 4   C m _ 2 Therefore, the surface charge density on the cube is: _ = 0.4 _ 10 _ 3   C m _ 2 So, the correct answer is: Option D: 0.4 _ 10 _ 3 C m _ 2

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