Question

Electro field is given by E = AX + B where A = 20, B = 10, Potential at x = 1 is V1 and
potential at x = -5 is V2 calculate V1-V2.
[JEE-MAINS 20191
1) 320 V
2) 180 V
3) 280 V
4) 350 V
pls reply with proper explanation​

Answer 1

Here the electric field,

$\sf{\longrightarrow E=ax+b}$

where $\sf{a=20}$ and $\sf{b=10.}$ So,

$\sf{\longrightarrow E=20x+10}$

Since $\sf{E}$ only depends upon $\sf{x,}$

$\sf{\longrightarrow-\dfrac{dV}{dx}=20x+10}$

$\sf{\longrightarrow dV=-(20x+10)\ dx}$

Integrating,

• $\sf{V}$ is integrated from $\sf{V_2}$ to $\sf{V_1.}$

• $\sf{x}$ is integrated from $\sf{-5}$ to $\sf{1.}$

So,

$\displaystyle\sf{\longrightarrow\int\limits_{V_2}^{V_1}dV=-10\int\limits_{-5}^{1}(2x+1)\ dx}$

$\displaystyle\sf{\longrightarrow V_1-V_2=-10\left[x^2+x\right]_{-5}^1}$

$\displaystyle\sf{\longrightarrow V_1-V_2=-10\left(1^2+1-(-5)^2-(-5)\right)$

$\displaystyle\sf{\longrightarrow V_1-V_2=-10\left(1+1-25+5\right)$

$\displaystyle\sf{\longrightarrow\underline{\underline{V_1-V_2=180\ V}}$