If curl of a vector function is zero then this vector function can describe the electric field. Using this idea, check which is an impossible electrostatic field. a) E = K[(xy)î + (2yz)j +(3xz)k] b) E = K[(y²)î + (2xy +z²)j + (2yz)k] Here, K is a constant with appropriate units.
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![If curl of a vector function is zero then this vector function can describe the
electric field. Using this idea, check which is an impossible electrostatic field.
a) E = K[(xy)î + (2yz)j +(3xz)k]
b) E = K[(y²)î + (2xy +z²)j + (2yz)k]
Here, K is a constant with
appropriate units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F849d30cd-96b5-430d-9e8a-285163e1ba99%2F94a1be7d-831c-4046-8266-9e6eaf6fcba2%2Fou2ospc.png&w=3840&q=75)

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- Assume you have a line of positive charge with a linear charge density of 10.0 µC/m. Assume that this line of charge is infinitely long and lies on the z-axis (which is perpendicular to both the x- and y-axes). a) Find the strength and direction of the electric field associated with this line of charge at (0.5 m, 0 m, 0 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z b) Find the strength and direction of the electric field associated with this line of charge at (0 m, 0.5 m, 5 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z c) Find the strength and direction of the electric field associated with this line of charge at (2.0 m, 0 m, Om) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+zA charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).Consider two charges q1=−40e and q2=−48e at positions (48,−46,29) and (32/√3, −10/√2 ,21) respectively where all the coordinates are measured in the scale of 10-9 m or nano meters. If position vector of the charge q1 is r⃗ 1 and charge q2 is r⃗ 2. Now consider another charge q3=−47e is in the xyz system positioned at (−41/√3, 42/√2, 35). Calculate the net force acting on q1 and q2. c) Net Force on q1 due to other charges x component of the force y component of the force z component of the force d) Net Force on q2 due to other charges x component of the force y component of the force z component of the force
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