1.

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 pointof 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»

\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{<klux>ANSWER</klux>}}} \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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