Two point charges A and B of values 5*10C and 3*10C are kept 6cm apart in air .calculate the work done when charge B is moved by 1cm towards charge A .  [ with simple explanation and diagram ] 

Asked by yash.bisht9910 | 6th Jun, 2015, 12:17: PM

Expert Answer:

 
Given that:
begin mathsize 14px style straight q subscript 1 space equals space 5 cross times space 10 to the power of negative 9 end exponent space straight C space semicolon space straight q subscript 2 space equals space 3 cross times space 10 to the power of negative 9 end exponent space straight C Initial space distance space between space the space charges space equals space straight r subscript 1 space equals space 6 space cm space equals space 6 cross times 10 to the power of negative 2 end exponent space straight m space Final space distance space between space the space charges space equals space straight r subscript 2 space equals space 5 cm space equals space 5 cross times 10 to the power of negative 2 space end exponent straight m Work space done space in space moving space the space charge space is space equal space to space the space gain space in space the space electrostatic space potential space of space the space system. Initial space potential space energy comma space straight U subscript 1 space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r subscript 1 end fraction Final space potential space energy comma space straight U subscript 2 space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r subscript 2 end fraction Therefore comma space the space work space done comma space straight W space equals space straight U subscript 2 space minus space straight U subscript 1 straight W space equals space fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 πε subscript straight o end fraction open square brackets 1 over straight r subscript 2 minus 1 over straight r subscript 1 close square brackets Substituting space the space values comma space we space get colon straight W space equals 9 space cross times space 10 to the power of 9 space cross times space open parentheses 5 cross times space 10 to the power of negative 9 end exponent space cross times space 3 cross times space 10 to the power of negative 9 end exponent close parentheses space cross times space open square brackets fraction numerator 1 over denominator 5 cross times 10 to the power of negative 2 end exponent end fraction minus fraction numerator 1 over denominator 6 cross times 10 to the power of negative 2 end exponent end fraction close square brackets straight W equals 135 space cross times space 10 to the power of negative 7 end exponent space cross times space open square brackets fraction numerator 6 minus 5 over denominator 30 end fraction close square brackets straight W space equals space 4.5 space cross times space 10 to the power of negative 7 end exponent space straight J end style
Note: The values of the charges A and B provided are incorrect. So kindly refer to the values used by us for solving the problem.

Answered by Yashvanti Jain | 13th Dec, 2017, 07:58: PM