What is the electric field at the point x = 3.5 m, y = 2.0 m?

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SUMMARY

The electric potential in the given region is defined by the equation V = axy, with a = 1.7 V/m². At the point (x = 3.5 m, y = 2.0 m), the electric potential calculates to V = 11.9 V. The electric field (E) can be derived from the potential using the relation E = -∇V, resulting in E = -1.7 (2i + 3.5j) V/m in unit vector notation. For a particle with mass m = 1.67 × 10-27 kg and charge q = +1.6 × 10-19 C, the initial acceleration is determined using F = ma, yielding a magnitude of 1.52 × 1011 m/s².

PREREQUISITES
  • Understanding of electric potential and electric fields
  • Familiarity with unit vector notation
  • Knowledge of Newton's second law (F = ma)
  • Basic algebra for calculations involving variables
NEXT STEPS
  • Study the relationship between electric potential and electric field in detail
  • Learn about gradient operators in vector calculus
  • Explore applications of Newton's second law in electric fields
  • Investigate the behavior of charged particles in electric fields
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Students in physics, particularly those studying electromagnetism, as well as educators and anyone seeking to understand the relationship between electric potential and electric fields.

Bri15
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1. Homework Statement [/b]

The electric potential in a region of space is given by V = axy where a = 1.7 V/m2.

(a) What is the electric field at the point x = 3.5 m, y = 2.0 m? Give your answer in unit
vector notation.

(b) If a particle of mass m = 1.67 × 10 −27 kg and charge q = +1.6 × 10 −19 C is released from
this point, what is the magnitude of its initial acceleration?

Homework Equations



V=axy

The Attempt at a Solution


(a)V=(1.7)(3.5)(2)
11.9
This seems to simple is this correct. Also do not understand unit vector notation.
(b) unsure of the equation to use
 
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Bri15 said:
1. Homework Statement [/b]

The electric potential in a region of space is given by V = axy where a = 1.7 V/m2.

(a) What is the electric field at the point x = 3.5 m, y = 2.0 m? Give your answer in unit
vector notation.

(b) If a particle of mass m = 1.67 × 10 −27 kg and charge q = +1.6 × 10 −19 C is released from
this point, what is the magnitude of its initial acceleration?

Homework Equations



V=axy

The Attempt at a Solution


(a)V=(1.7)(3.5)(2)
11.9
This seems to simple is this correct. Also do not understand unit vector notation.
(b) unsure of the equation to use

(a) What's the formula for the electric field, given the potential?
(b) F = ma
 
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