A charge Q is distributed over three concentric spherical shells of radii a , b , c a < b < c such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a , would be:

Q a + b + c 4 π ϵ 0 a 2 + b 2 + c 2

Q a 2 + b 2 + c 2 4 π ϵ 0 a 3 + b 3 + c 3

Q 12 π ϵ 0 a b + b c + c a a b c

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 125

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The electric field and the electric potential at a point are $E$ and $V$ , respectively.

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Important Questions on Electrostatics

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 126

The electric field in a region is directed outward and proportional to the distance

r

from the origin. Taking the electric potential at the origin to be zero, the electric potential at a distance

r

.

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 128

A point charge is located at

O .

There is a point

P

at a distance

r

from it. The electric field at point

P

is

500 V m^{- 1}

and potential is

3000 V .

The value of

r

is ?

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 129

Figure shows three points $A, B$ and $C$ in a region of uniform electric field $\vec{E} .$ The line $A B$ is perpendicular and $B C$ is parallel to the field lines. Then which of the following holds good?

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 130

The variation of potential with distance $r$ from a fixed point is shown in the figure. The electric field at $r = 3 cm$ is:

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 131

The electric potential at any point is

V = - 5 x + 3 y + \sqrt{15} z

. Then the magnitude of the electric field is

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 132

The potential at a point

x

(measured in

μm

) due to some charges situated on the

x

-axis is given by

V (x) = 20 / (x^{2} - 4) volts

. The electric field

E

at

x = 4 μm

is given by

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-1>Q 133

The electric potential $V$ as a function of distance $x$ (in $metre$ ) is given by $V = (5 x^{2} + 10 x - 9) volt$ . The value of the electric field at $x = 1 m$ would be