A point charge is at the origin. With this point charge as...

A point charge is at the origin. With this point charge as the source point, what is the unit vector $\hat{r}$ in the direction of the field point (a) at $x=0, y=-1.35 \mathrm{~m}$ (b) at $x=12.0 \mathrm{~cm}, y=12.0 \mathrm{~cm} ;$ (c) at $x=-1.10 \mathrm{~m}, y=2.60 \mathrm{~m} ?$ Express your results in terms of the unit vectors $\hat{\imath}$ and $\hat{\jmath}$

A point charge is at the origin. With this point charge as the source point, what is the unit vector $\hat{r}$ in the direction of the field point
(a) at $x=0, y=-1.35 \mathrm{~m}$
(b) at $x=12.0 \mathrm{~cm}, y=12.0 \mathrm{~cm} ;$ (c) at $x=-1.10 \mathrm{~m}, y=2.60 \mathrm{~m} ?$ Express your results in terms of the unit vectors $\hat{\imath}$ and $\hat{\jmath}$

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Key Concepts

Unit Vector

A unit vector is a vector with a magnitude of 1 that indicates direction. It is obtained by dividing any vector by its magnitude, thereby normalizing it to have a unit length.

Position Vector

A position vector specifies the location of a point in space relative to an origin, using its components along the coordinate axes (typically represented as x and y components in two dimensions). It provides the necessary displacement from the source point to the field point.

Vector Magnitude

The magnitude of a vector is the length or size of the vector, calculated as the square root of the sum of the squares of its components (i.e., ?(x² + y²) in a two-dimensional space). This is essential for normalizing a vector to form a unit vector.

Representation in Cartesian Coordinates

Any vector in a two-dimensional plane can be expressed in terms of the Cartesian unit vectors î and ?, which correspond to the x and y directions respectively. This representation makes it straightforward to describe vector directions and perform vector operations.

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