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The electric potential V in a region of space is given by V(x,y,z) = A(x² – 3y² + z²) where A = 4.00×10-³ J/(C-m²). a) What is the electric field at the point (1.00 m, 1.00 m, 1.00 m)? b) If an 8.854 x 10-12 kg test charge of +1.50 µC were placed at the point (0, 0, 1.00 m) and released from rest, will it move toward the origin or away from the origin? Explain. c) After starting from rest at the point (0, 0, 1.00 m), what will be the speed of the test charge after it has traveled 1.00 m along the z-axis?

The electric potential V in a region of space is given by V(x,y,z) = A(x² – 3y² + z²) where A = 4.00×10-³ J/(C-m²). a) What is the electric field at the point (1.00 m, 1.00 m, 1.00 m)? b) If an 8.854 x 10-12 kg test charge of +1.50 µC were placed at the point (0, 0, 1.00 m) and released from rest, will it move toward the origin or away from the origin? Explain. c) After starting from rest at the point (0, 0, 1.00 m), what will be the speed of the test charge after it has traveled 1.00 m along the z-axis?

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The electric potential \( V \) in a region of space is given by \[ V(x, y, z) = A(x^2 - 3y^2 + z^2) \] where \( A = 4.00 \times 10^{-3} \, \text{J/(C} \cdot \text{m}^2) \). **a)** What is the electric field at the point \( (1.00 \, \text{m}, 1.00 \, \text{m}, 1.00 \, \text{m}) \)? **b)** If an \( 8.854 \times 10^{-12} \, \text{kg} \) test charge of \( +1.50 \, \mu\text{C} \) were placed at the point \( (0, 0, 1.00 \, \text{m}) \) and released from rest, will it move toward the origin or away from the origin? Explain. **c)** After starting from rest at the point \( (0, 0, 1.00 \, \text{m}) \), what will be the speed of the test charge after it has traveled \( 1.00 \, \text{m} \) along the z-axis?
Transcribed Image Text:The electric potential \( V \) in a region of space is given by \[ V(x, y, z) = A(x^2 - 3y^2 + z^2) \] where \( A = 4.00 \times 10^{-3} \, \text{J/(C} \cdot \text{m}^2) \). **a)** What is the electric field at the point \( (1.00 \, \text{m}, 1.00 \, \text{m}, 1.00 \, \text{m}) \)? **b)** If an \( 8.854 \times 10^{-12} \, \text{kg} \) test charge of \( +1.50 \, \mu\text{C} \) were placed at the point \( (0, 0, 1.00 \, \text{m}) \) and released from rest, will it move toward the origin or away from the origin? Explain. **c)** After starting from rest at the point \( (0, 0, 1.00 \, \text{m}) \), what will be the speed of the test charge after it has traveled \( 1.00 \, \text{m} \) along the z-axis?
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