Question

An infinite number of charges each equal to q is placed along x axis at x = 1, x = 2, x = 4, x = 8, x = 16…….. If the electric field at the origin due to these charges is 12000 N/C then value of q is : [sum of infinite G.P. is S = $\frac{a}{1 - r}$]

• A. 1mC
• B. 1 mC
• C. 1 nC
• D. 1 C

Answer 1

Answer: (A)

1mC

Answer 2

E₀ = + +$\frac { \mathrm { kq } } { 4 ^ { 2 } }$+$\frac { \mathrm { kq } } { 8 ^ { 2 } }$………….

E = kq $\left( 1 + \frac { 1 } { 4 } + \frac { 1 } { 16 } + \frac { 1 } { 64 } + \ldots \ldots \infty \right)$E = kq = kq . $\frac { 1 } { 1 - \left( \frac { 1 } { 4 } \right) }$=

12 × 10³ = $\frac { 9 \times 10 ^ { 9 } \times 4 } { 3 }$× q \ q = 1mC