This question is incomplete, the complete question is;
What is the magnitude of the electric field at the point (8.70i - 9.10j + 7.20k ) m if the electric potential is given by V = 4.30xyz², where V is in volts and x, y and z are in meters.
Answer:
the magnitude of the electric field is 5648.67 N/C
Explanation:
Given the data in the question;
Suppose electric field at this point is;
E = Exi + Eyj + Ezk
Now, electric field is given by;
E = -dV/dr
so,
Ex = -d( 4.30xyz² )/dx = -4.30yz²
Ey = -d( 4.30xyz² )/dy = -4.30xz²
Ez = -d( 4.30xyz² )/dz = -8.60xyz
so
E = -4.30yz² i - 4.30xz² j - 8.60xyz k
now, at the point (8.70i - 9.10j + 7.20k )
E = (-4.30(-9.10)(7.20)²) i + (-4.30(8.70)(7.20)²) j + (-8.60(8.70)(-9.10)(7.20) k
E = 2028.499 i - 1939.334 j + 4902.206 k
so, Magnitude of electric field will be;
|E| = √( Ex² + Ey² + Ez² )
we substitute
|E| = √( (2028.499)² + (-1939.334)² + (4902.206)² )
|E| = √( 31907448.222993 )
|E| = 5648.67 N/C
Therefore, the magnitude of the electric field is 5648.67 N/C
