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**Question**

The potential as a function of position in a region is given by V(x)=3x-2x2-x3.with x in meters and V in volts.

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**Question**

The potential as a function of position in a region is given by V(x)=3x-2x2-x3.with x in meters and V in volts.

** **

**Solution**

V(x) = 3x - 2x^2 - x^3

a)

Point where V =0

3x - 2x^2 - x^3 = 0

-(x-1) x (x +3) = 0

On solving above equation we get -

x = -3 , 0 & 1

**Values of X where V =0 are -**

**x = -3**

**x = 0**

**x = 1**

(b)

Electric Field E = - d/dx(V)

E = - d/dx( 3x - 2x^2 - x^3)

E = - (3 - 4x -3x^2)

E = -3 + 4x + 3x^2

**Expression for Electric field , E = -3 + 4x + 3x^2**

(c)

Points on X axis Where , E =0

-3 + 4x + 3x^2 = 0

On solving above equation we get -

x = -1.87 & 0.53

**Values of X where E =0 are -**

**x = -1.87**

**x = 0.53**

** **

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