Question

Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be:

विकल्प

• 1 : 2

• 2 : 1

• 1 : 1

• 1 : 4

Answer 1

2 : 1

Explanation:

Since, V_A = V_B

⇒ `"kQ"_"A"/"R"_"A" = "kQ"_"B"/"R"_"B"`

Here, K = `1/(4piepsilon_0)`

⇒ `"Q"_"A"/"Q"_"B" = "R"_"A"/"R"_"B"=1/2`

`"E"_"A" = "kQ"_"A"/"R"_"A"^2; "E"_"B" = "kQ"_"B"/"R"_"B"^2`

⇒ `"E"_"A"/"E"_"B"= "Q"_"A"/"Q"_"B"xx"R"_"B"^2/"R"_"A"^2`

= `"R"_"B"/"R"_"A"`

= `2/1`