Question

# The electric potential in a certain region along the x-axis varies with x according to the relation V(x)=5−4x2. Then, the correct statement is :

A
the potential difference between the points x=1m and x=2m is 12 Volt
B
the force experienced by a Coulomb of charge placed at x=1 m is 8 Newton
C
the electric field components along Y and Z direction are zero
D
all of the above
Solution
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#### V(x)=5−4x2V(1)=5−4=1V,V(2)=5−4(22)=−11VPotential difference between x=1m and x=2m is V12=V1−V2=1−(−11)=12Vhere, Ex=−dVdx=8x,Ey=−dVdy=0 and Ez=−dVdz=0The electric force on 1 coulomb charge at x=1 is F=qEx=1(8)=8N

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