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a spere of radius 0.1cm is charged to 300v the force a ting per unit area is

Asked by slavanya19102005 | 18 Nov, 2023, 08:29: PM

Expert Answer

If a sphere of 0.1 cm is charged to potential 300 V .

Potential V on the surface of charged sphere is

begin mathsize 14px style V space equals space K space cross times q over R space equals space 300 end style

where K = 1/(4πε_o) = 9 × 10⁹ N m² C^-2 is Coulomb's constant.

Hence charge on the sphere is

begin mathsize 14px style q space equals space fraction numerator 300 space cross times space R over denominator K end fraction space equals space fraction numerator 300 space cross times space 0.1 space cross times 10 to the power of negative 2 end exponent over denominator 9 space cross times 10 to the power of 9 end fraction space C space equals space 1 third cross times 10 to the power of negative 10 end exponent space C end style

Intensity of Electric field is electrostatic force per unit charge.

Hence we can consider force per unit area as Electric field E divided by surface area of sphere 4πR² .

Force per unit area =

begin mathsize 14px style fraction numerator E over denominator 4 pi R squared end fraction space equals K space cross times q over R squared cross times fraction numerator 1 over denominator 4 pi R squared end fraction space end style

Force per unit area =

begin mathsize 14px style fraction numerator E over denominator 4 pi R squared end fraction space equals space 9 space cross times 10 to the power of 9 cross times 1 third cross times 10 to the power of negative 10 end exponent cross times fraction numerator 1 over denominator 4 pi space cross times space left parenthesis 0.1 right parenthesis to the power of 4 end fraction space N space C to the power of negative 1 end exponent m to the power of negative 2 end exponent end style

Force per unit area = 239 N C^-1 m^-2

Answered by Thiyagarajan K | 18 Nov, 2023, 09:24: PM

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