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  • (a) Two point charges  and are kept <img alt="r" src="https://learn.careers360.com/latex-ima

(a) Two point charges q_{1} and q_{2} are kept rdistance apart in a uniform external electric field \vec{E}. Find the amount of work done in
assembling this system of charges.

(b) A cube of side 20\; cm is kept in a region as shown in the figure. An electric field \vec{E} exists in the region such that the potential at a point is given by V=10x+5, where Vis in volt and x is in m.

Find the
(i) electric field \vec{E}, and

(ii) total electric flux through the cube.

 

 
 
 
 
 

Answers (1)

a) The work done in bringing charge q1 from infinity to r1 is

W_1=q_1V_1

The work done in bringing charge q2 from infinity to r2 is

W_2=q_2V_2

Work done in moving q2 against the field due to q1

W_3=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}

Total work

\\W=W_1+W_2+W_3\\\\=q_1V_1+q_2V_2+\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}

b) E=-dV/dx

=-10V/m

(ii) Electric flux through the cubec= the sum of electric flux through 6 faces
The electric flux through faces perpendicular Y and Z axis=0 (E is along the x-axis)
The electric flux through faces perpendicular to X-axis
=10(0.2)^2-10(0.2)^2=0

Posted by

Safeer PP

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