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A positive charge of 1.5 muC is moving w...

A positive charge of 1.5 `mu`C is moving with a speed of `2 xx 10^(-6) ms^(-1)` along the postive X-axis. A magnetic field, `vec(B) = (0.2 hat(j) + 0.4 hat(k))` tesla acts in space. Find the magnetic force acting on the charge.

Text Solution

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Here q = 1.5`mu`C = 1.5 `xx 10^(-6)` C
`vec(v) = 2xx 10^(6) hat(i) ms^(-1) : vec(B) = (0.2 hat(j) + 0.4 hat(k))`T
Magnetic force on the positive charge is
`vec(F) = q (vec(v) xx vec(B))`
= `1.5 xx 10^(-6) [ 2 xx 10^(6) hat(i) xx (0.2 hat(j) + 0.4 hat(k)) ] `
= 3.0` [ 0.2 hati xx hatj + 0.4 hati xx hatk ]`
`= (0.6 hatk - 1.2 hatj ) N" " [ because i xx hatj = hatk, hati xx hatk = - hatj]`
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