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:
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:
Show Hint
Electric field is always the negative gradient of potential.
Updated On: Mar 18, 2026
- 6√(5)N
- 30N
- 24N
- 4√(35)N
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The Correct Option is D
Solution and Explanation
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)
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