Question

In a region, the potential is represented by V(x,y,z)=6x-8xy-8y+6yz, where V is in volts and x,y,z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is:

• A. 6√(5)N
• B. 30N
• C. 24N
• D. 4√(35)N

Hint:

Electric field is always the negative gradient of potential.

Answer 1

The Correct Option is D

Step 1: Electric field is given by E=- V
Step 2: ( V)/( x)=6-8y, ( V)/( y)=-8x-8+6z, ( V)/( z)=6y
Step 3: At (1,1,1): E=(2,10,-6)
Step 4: Force F=qE=2(2,10,-6)=(4,20,-12)
Step 5: |F|=√(4²+20²+12²)=√(560)=4√(35)