Question

A rod of length 2.4 m and radius 4.6 a negative charge of 4.2 x 10-7 C spread uniformly over it surface. The electric field near the mid point
of the rod, at a point on its surface is (a) -8.6 x 105NC-1 (b) 8.6 x 104 (c) - 6.7 x 105NC-1 (d) 6.7 x 104
​

Answer 1

$\huge \blue{ \underline \purple{ \underline \mathtt \red{Question}}} \orange \downarrow$

A rod of length 2.4m and radius 4.6mm carries a negative charge of 4.2 × $\tt\green{10}^\green{−7}$C spread uniformly over it surface. The electric field near the mid-point of the rod, at a point on its surface is:

(a) $\tt\orange{- 8.6 \: \times \: {10}^{5} {NC}^{ - 1}}$

(b) $\tt\orange{- 8.6 \: \times \: {10}^{4} {NC}^{ - 1}}$

(c) $\tt\orange{- 6.7 \: \times \: {10}^{5} {NC}^{ - 1}}$

(d) $\:\:$ $\tt\orange{ 6.7 \: \times \: {10}^{4} {NC}^{ - 1}}$

$\huge \blue{ \underline \purple{ \underline \mathtt \red{Answer}}} \orange \downarrow$

Correct option is Ⓒ $\tt\blue{ - 6.7 \: \times \: {10}^{5} {NC}^{ - 1} }$

Here,

$\tt{l \: \longmapsto \: 2.4m \: , \: r \: = \: 4.6mm \: \longmapsto \: 4.6 \: \times \: {10}^{ - 3}m}$

$\tt{q \: \longmapsto \: 4.6 \: \times \: {10}^{ - 7} C}$

Linear charge density,

$\tt{λ \: \longmapsto \: \frac{q}{1} \: \longmapsto \: \frac{ - 4.2 \: \times \: {10}^{ - 7} }{2.4}}$

$\tt{ \: \longmapsto \: - 1.75 \: \times \: {10}^{ - 7} {Cm}^{ - 1}}$

Electric field,

$E \: \longmapsto \: \frac{λ}{2 \pi \: e_0r} \:$

$\tt={ \frac{ - 1.75 \: \times \: {10}^{ - 7} }{2 \: \times \: 3.14 \: \times \: {10}^{ - 12 \: \times \: 4.6 \: \times \: {10}^{ - 3} } } \: \leadsto \: - 6.67 \: \times \: {10}^{5} {NC}^{ - 1} }$

I hope it's helps you ☺️.

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