A metal cube of side 5 cm is charged with . The surface charge density on the cube is [2024]

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Q.
A metal cube of side 5 cm is charged with $6$ $μC$ . The surface charge density on the cube is [2024]

1 $0.125 \times 10^{- 3} C$ $m^{- 2}$

2 $0.25 \times 10^{- 3} C$ $m^{- 2}$

3 $4 \times 10^{- 3} C$ $m^{- 2}$

4 $0.4 \times 10^{- 3} C$ $m^{- 2}$

Ans.
(4)

Given, charge $(q) = 6$ $μ C = 6 \times 10^{- 6} C$

Length of cube, $(l) = 5$ $cm = 0.05$ $m$

Total surface area of cube,

$(s) = 6 l^{2} = 6 \times {(10.05)}^{2} = 0.015$ $m^{2}$

Surface charge density, $(σ) = \frac{Total charge}{Total area}$

$= \frac{6 \times 10^{- 6}}{0.015} = 0.4 \times 10^{- 3}$ $c m^{- 2}$

Solution

Q.
A metal cube of side 5 cm is charged with $6$ $μC$ . The surface charge density on the cube is [2024]

1 $0.125 \times 10^{- 3} C$ $m^{- 2}$

2 $0.25 \times 10^{- 3} C$ $m^{- 2}$

3 $4 \times 10^{- 3} C$ $m^{- 2}$

4 $0.4 \times 10^{- 3} C$ $m^{- 2}$

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Solution

Q. A metal cube of side 5 cm is charged with 6 μC. The surface charge density on the cube is [2024]

1 0.125×10-3C m-2

2 0.25×10-3C m-2

3 4×10-3C m-2

4 0.4×10-3C m-2

Ans. (4) Given, charge (q)=6μC=6×10-6C Length of cube, (l)=5 cm=0.05 m Total surface area of cube, (s)=6l2=6×(10.05)2=0.015 m2 Surface charge density, (σ)=Total chargeTotal area =6×10-60.015=0.4×10-3 cm-2

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Q.
A metal cube of side 5 cm is charged with $6$ $μC$ . The surface charge density on the cube is [2024]

1 $0.125 \times 10^{- 3} C$ $m^{- 2}$

2 $0.25 \times 10^{- 3} C$ $m^{- 2}$

3 $4 \times 10^{- 3} C$ $m^{- 2}$

4 $0.4 \times 10^{- 3} C$ $m^{- 2}$