Question
A ring of charge with radius $$0.5\,m$$ has $$0.002\,\pi m$$ gap. If the ring carries a charge of $$+1\,C,$$ the electric field at the centre is
A ring of charge with radius $$0.5\,m$$ has $$0.002\,\pi m$$ gap. If the ring carries a charge of $$+1\,C,$$ the electric field at the centre is
A.
$$7.5 \times {10^7}N{C^{ - 1}}$$
B.
$$7.2 \times {10^7}N{C^{ - 1}}$$
C.
$$6.2 \times {10^7}N{C^{ - 1}}$$
D.
$$6.5 \times {10^7}N{C^{ - 1}}$$
Answer :
$$7.2 \times {10^7}N{C^{ - 1}}$$
Solution :
Charge on the element opposite to the gap is
$$\eqalign{ & dq = \frac{Q}{{2\pi r}}\left( {0.002\pi } \right) \cr & = \frac{1}{{2\pi \left( {0.5} \right)}} \times \frac{{2\pi }}{{1000}} = 2 \times {10^{ - 3}}C \cr & E = \frac{{9 \times {{10}^9} \times 2 \times {{10}^{ - 3}}}}{{{{\left( {0.5} \right)}^2}}} = 7.2 \times {10^7}N{C^{ - 1}} \cr} $$
Charge on the element opposite to the gap is
$$\eqalign{ & dq = \frac{Q}{{2\pi r}}\left( {0.002\pi } \right) \cr & = \frac{1}{{2\pi \left( {0.5} \right)}} \times \frac{{2\pi }}{{1000}} = 2 \times {10^{ - 3}}C \cr & E = \frac{{9 \times {{10}^9} \times 2 \times {{10}^{ - 3}}}}{{{{\left( {0.5} \right)}^2}}} = 7.2 \times {10^7}N{C^{ - 1}} \cr} $$
