Question

If a cube of side 5 cm has a charge of 6 microcoulombs, then the surface charge density is:
(a) 4  102 C/m2
(b) 4  102 C/m2
(c) 4  103 C/m2
(d) 4  103 C/m

Answer 1

Given that ,

• Side of cube = 5 cm or 5 × (10)^-2 m
• Charge (q) = 6 μc or 6 × (10)^-6 c

We know that ,

$\large \sf \fbox{Surface \: charge \: density = \frac{Charge}{Area} }$

Thus ,

$\sf \mapsto Surface \: charge \: density = \frac{6 \times {(10)}^{ - 6} }{6 \times {(5 \times {(10)}^{ - 2}) }^{2} } \\ \\\sf \mapsto Surface \: charge \: density = \frac{ {(10)}^{ - 2} }{25} \\ \\\sf \mapsto Surface \: charge \: density = 0.4 \times {(10)}^{ - 3} \: \: c/ {m}^{2}$

$\sf \therefore \underline{The \: surface \: charge \: density \: is \: 0.4 \times {(10)}^{ - 3} \: \: c/ {m}^{2} }$